identifying the diffusion coefficient by optimization from the final observation this paper deals with the inverse problem of determining a pair a u in the reaction diffusion equationu t au x x f x t with initial and boundary conditionsu x 0 email protected x u x x 0 u x x 1 0 from the final measurement data u x t z x which has important application in a large fields of applied science based on the optimal control framework the existence uniqueness and stability of the minimizer for the cost functional are established a necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced the gradient iteration algorithm is applied to the inverse problem and some numerical results are presented for various typical test examples

modeling long memory in stock market volatility inspired by the idea that regime switching may give rise to persistence that is observationally equivalent to a unit root we derive a regime switching process that exhibits long memory the feature of the process that generates long memory is a heavy tailed duration distribution using this process for volatility we obtain a regime switching stochastic volatility rssv model that we fit to daily s p returns from 1928 through 1995 by means of the efficient method of moments estimation emm method forecasts of rssv volatility given past returns can be generated by reprojection as we illustrate the rssv model is accepted according to the emm chi squared statistic using this statistic we also evaluate several other models that have been proposed in the literature and some modifications to them we find that models that exhibit long memory in volatility and heavy tails conditionally as does the rssv model fit the data whereas models without these characteristics do not we also find weak evidence that suggests the presence of an additional short memory component of volatility over and above the long memory component

a splitting up algorithm for the determination of the control parameter in multi dimensional parabolic problem one of the global approaches for solving the two dimensional inverse parabolic problem is the predictor corrector which takes place for evaluating the pair u p and adjusting the evaluation for the desired accuracy for general class of higher dimensional parabolic problems the adi or the fs methods have been considered with an advantage of reducing or splitting the problem in accordance to the time fractions into one dimensional dependent problems and they are a non parallel type of splittings in 1992 lu et al proposed an additive parallel type of splitting method such that the splitting is defined in accordance to the spatial variables to solve multi dimensional parabolic problem in this work we will present a new algorithm for solving two or higher dimensional inverse control problem the algorithm is a parallel predictor corrector type of method such that the solution and the predictor and corrector schemes are defined by the parallel splitting up method some numerical results from the solution of two model problems are considered to demonstrate the accuracy of the presented algorithm

control parameter estimation in a semi linear parabolic inverse problem using a high accurate method abstract parabolic inverse problems have an important role in many branches of science and technology the aim of this research work is to solve these classes of equations using a high order compact finite difference scheme we consider the following inverse problem for finding u x t and p t governed by u t u xx p t u x t with an over specified condition inside the domain spatial derivatives are approximated using central difference scheme the time advancement of the simulation is performed using a third order compact runge kutta method the convergence orders for the approximation of both u and p are of o k 3 h 2 which improves the results obtained in the literature an exact test case is used to evaluate the validity of our numerical analysis we found that the accuracy of the results is better than that of previous works in the literature

numerical solution of fractional partial differential equations with variable coefficients using generalized fractional order legendre functions abstract in this paper a general formulation for the generalized fractional order legendre functions gflfs is constructed to obtain the numerical solution of fractional partial differential equations with variable coefficients the special feature of the proposed approach is that we define generalized fractional order legendre functions over 0 h based on fractional order legendre functions we use these functions to approximate the unknown function on the interval 0 h 0 l in addition the gflfs fractional differential operational and product matrices are driven these matrices combine with tau method to transform the problem to solve systems of linear algebraic equations by solving the linear algebraic equations we can obtain the numerical solution the error analysis shows that the algorithm is convergent the method is tested on examples the results show that the gflfs yields better results

on solving systems of multi pantograph equations via spectral tau method abstract the current manuscript focuses on solving systems of multi pantograph equations the spectral tau method is applied for solving systems of multi pantograph equations with shifted jacobi polynomials as basis functions the convergence analysis of the proposed technique is also investigated we introduced the numerical solutions of some test problems and compared the obtained numerical solutions of such problems with those given using different numerical methods

spectral element discretization of the maxwell equations on considere un probleme variationnel equivalent aux equations de l electromagnetisme avec conditions aux limites absorbantes sur une partie de la frontiere qu on prouve etre bien pose puis on propose une discretisation de ce probleme par schema aux differences finies en temps et elements spectraux en espace et on etablit des estimations d erreur entre solutions exacte et approchee

bounds on the kth eigenvalues of trees and forests abstract we prove the upper bound k t n k 1 for the kth largest eigenvalue of a tree t 1 k n 2 and show that this bound is best possible when n 0 mod k we further obtain the strict inequality t 1 k 1 t 1 k t t 1 where t n k for the case n 0 mod k 2 k n 2 our upper bound is also proved to be the best possible upper bound for the kth largest eigenvalues of the forests in all cases

remediation of contaminated groundwater by meshless local weak forms in this paper four meshless local weak form methods such as direct meshless local petrovgalerkin method dmlpg meshless local petrovgalerkin method mlpg local weak radial point interpolation method lwrpim and local weak moving kriging method lwmk are applied to find the numerical solution of coupled non linear advectiondiffusionreaction system arising in the prevention of groundwater contamination problem a comparison between these methods is done from the perspective of accuracy and computational efficiency an efficient fourth order exponential time differencing rungekutta method is utilized for the time discretization the computational efficiency is the most significant advantage of the dmlpg method in comparison with the other meshless local weak form methods because dmlpg reduces the computational costs significantly this is due to the fact that dmlpg shifts the numerical integrations over low degree polynomials rather than over complicated shape functions the main aim of this paper is to show that the meshless local weak form methods can be used for solving the system of non linear partial differential equations especially coupled non linear advectiondiffusionreaction system the numerical results confirm the good efficiency of the proposed methods for solving our model

dmlpg method for specifying a control function in two dimensional parabolic inverse pdes abstract this article describes a fast meshless technique the direct meshless local petrov galerkin dmlpg method for identifying a control function in two dimensional parabolic inverse pdes the dmlpg method is a truly meshless technique that directly approximates the local weak forms in dmlpg the local integrations are done over the low degree polynomial basis functions instead of the complicated shape functions thus the mass and stiff matrices are constructed by integration against polynomials this feature overcomes the main drawback of meshless methods in comparison with the finite element methods fem and significantly increases the computational efficiency in comparison with the other meshless weak form methods in this paper we apply the dmlpg and mlpg methods for solving two dimensional parabolic inverse pdes on regular and irregular domains these methods are compared with each other and the superiority of the dmlpg over the classical mlpg is demonstrated the numerical results confirm the good efficiency of the dmlpg method for solving inverse problems especially coefficient inverse problems finally we will conclude that the dmlpg method can be considered as an attractive alternative to existing meshless weak form methods in solving inverse problems

rational legendre pseudospectral approach for solving nonlinear differential equations of lane emden type lane emden equation is a nonlinear singular equation in the astrophysics that corresponds to the polytropic models in this paper a pseudospectral technique is proposed to solve the lane emden type equations on a semi infinite domain the method is based on rational legendre functions and gauss radau integration the method reduces solving the nonlinear ordinary differential equation to solve a system of nonlinear algebraic equations the comparison of the results with the other numerical methods shows the efficiency and accuracy of this method

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose the oil palm frond a lignocellulosic material is a high yielding energy crop that can be utilized as a promising source of xylose it holds the potential as a feedstock for bioethanol production due to being free and inexpensive in terms of collection storage and cropping practices the aim of the paper is to calculate the concentration and yield of xylose from the acid hydrolysis of the oil palm frond through a fuzzy fractional kinetic model the approximate solution of the derived fuzzy fractional model is achieved by using a tau method based on the fuzzy operational matrix of the generalized laguerre polynomials the results validate the effectiveness and applicability of the proposed solution method for solving this type of fuzzy kinetic model a new fractional kinetic equation under uncertainty was addressed to depict the chemical reaction arising in palm oil frond an efficient numerical simulation based on a tau method was derived to solve the proposed kinetic equation different cases were solved to demonstrate the validity and efficiency of the proposed technique

bellman adomian solutions of nonlinear inverse problems in continuum physics abstract this paper develops a joint application of bellman s differential quadrature method and adomian s decomposition technique to the solution of some nonlinear inverse problems an application in nonlinear mechanics is also developed

numerical computation of a control function in a partial differential equation this study presents several finite difference schemes for solving the three dimensional parabolic equation with a control function these techniques are developed for indentifying u u x y z t and p p t the temperature parameter which satisfy u t 2u x 2 2u y 2 2u z 2 p t email protected x y z t in rx 0 t u x y z 0 f x y z x y z r 0 1 3 u is known on the boundary of r and also u x 0 y 0 z 0 t e t 0

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

on the kth laplacian eigenvalues of trees with perfect matchings abstract let t n be the set of all trees of order n with perfect matchings in this paper we prove that for any tree t t n its k th largest laplacian eigenvalue k t satisfies k t 2 when n 2 k and k t n 2 k 2 n 2 k 2 4 2 when n 2 k moreover this upper bound is sharp when n 0 mod 2 k

direct numerical method for an inverse problem of a parabolic partial differential equation a coefficient inverse problem of the one dimensional parabolic equation is solved by a high order compact finite difference method in this paper the problem of recovering a time dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently while many theoretical results regarding the existence and uniqueness of the solution are obtained the development of efficient and accurate numerical methods is still far from satisfactory in this paper a fourth order efficient numerical method is proposed to calculate the function u x t and the unknown coefficient a t in a parabolic partial differential equation several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method

quasi maximum likelihood estimation in conditionally heteroscedastic time series a stochastic recurrence equations approach this paper studies the quasi maximum likelihood estimator qmle in a general conditionally heteroscedastic time series model of multiplicative form xt t zt where the unobservable volatility t is a parametric function of xt 1 x t p t 1 t q for some p q 0 and zt is standardized i i d noise we assume that these models are solutions to stochastic recurrence equations which satisfy a contraction random lipschitz coefficient property these assumptions are satisfied for the popular garch asymmetric garch and exponential garch processes exploiting the contraction property we give conditions for the existence and uniqueness of a strictly stationary solution xt to the stochastic recurrence equation and establish consistency and asymptotic normality of the qmle we also discuss the problem of invertibility of such time series models 1 introduction gaussian quasi maximum likelihood estimation that is likelihood estimation under the hypothesis of gaussian innovations is a popular method which is widely used for inference in time series models however it is often a nontrivial task to establish the consistency and asymptotic normality of the quasi maximum likelihood estimator qmle applied to specific models and therefore an in depth analysis of the probabilistic structure generated by the model is called for a classical example of this kind is the seminal paper by hannan 18 on estimation in linear arma time series in this paper we study the qmle for a general class of conditionally heteroscedastic time series models which includes garch asymmetric garch and exponential garch recall that a garch p q generalized autoregressive conditionally heteroscedastic of order p q process 4 i s def ined by

on the stability and convergence of a difference scheme for an one dimensional parabolic inverse problem abstract the parabolic equation with the control parameter is a class of parabolic inverse problems and is nonlinear while determining the solution of the problems we shall determinate some unknown control parameter these problems play a very important role in many branches of science and engineering this article is devoted to the following parabolic initial and boundary problem with the control parameter u t 2u x2 p t u x t 0

the decomposition approach to inverse heat conduction adomian s decomposition approach is employed for solving some inverse boundary value problems in heat conduction further the mollification method is applied to deal with noisy input data and obtain a stable approximate solution

an inverse problem of finding a parameter in a semi linear heat equation we consider the following inverse problem of finding the pair u p which satisfies the following u1 uxx p t u f x t u ux p t 0 x 1 0 t t u x 0 u0 x 0 x 1 ux 0 t f t ux 1 t g t 0 t t and 01 x t u x t dx e t 0 t t where u0 f g f and e are known functions the existence uniqueness regularity and the continuous dependence of the solution upon the data are demonstrated

a new operational matrix for solving fractional order differential equations abstract fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations for that reason we need a reliable and efficient technique for the solution of fractional differential equations this paper deals with the numerical solution of a class of fractional differential equations the fractional derivatives are described in the caputo sense our main aim is to generalize the legendre operational matrix to the fractional calculus in this approach a truncated legendre series together with the legendre operational matrix of fractional derivatives are used for numerical integration of fractional differential equations the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem the method is applied to solve two types of fractional differential equations linear and nonlinear illustrative examples are included to demonstrate the validity and applicability of the presented technique

the use of chebyshev cardinal functions for the solution of a partial differential equation with an unknown time dependent coefficient subject to an extra measurement a numerical technique is presented for the solution of a parabolic partial differential equation with a time dependent coefficient subject to an extra measurement the method is derived by expanding the required approximate solution as the elements of chebyshev cardinal functions using the operational matrix of derivative the problem can be reduced to a set of algebraic equations from the computational point of view the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use

finding a control parameter in one dimensional parabolic equations an inverse problem concerning diffusion equation with source control parameter is considered several finite difference schemes are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain these schemes are based on the second order 3 point forward time centred space ftcs explicit formula and the fourth order 5 point ftcs explicit scheme and the second order 3 point backward time centred space btcs implicit technique and the fourth order 3 3 crandall s implicit formula the 5 point ftcs scheme has a bounded range of stability but its fourth order accuracy is significant the 3 point btcs method uses less central processor cpu time than the 3 3 crandall s technique but it is only second order accurate the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the results of a numerical experiment are presented and accuracy and the cpu time needed for the parabolic inverse problem are discussed

fully implicit finite differences methods for two dimensional diffusion with a non local boundary condition three new fully implicit methods which are based on the 5 5 crank nicolson method the 5 5 n h noye hayman implicit method and the 9 9 n h implicit method are developed for solving the heat equation in two dimensional space with non local boundary conditions the latter is fourth order while the others are second order while the implicit methods developed here like the scheme based on the standard implicit backward time centered space btcs method use a large amount of central processor cpu time the high accuracy of the new fourth order fully implicit scheme is significant like the btcs method the new methods are also unconditionally stable

identifying a control function in parabolic partial differential equations from overspecified boundary data determination of an unknown time dependent function in parabolic partial differential equations plays a very important role in many branches of science and engineering in the current investigation the adomian decomposition method is used for finding a control parameter p t in the quasilinear parabolic equation u t u x x p t email protected in 0 1 x 0 t with known initial and boundary conditions and subject to an additional condition in the form of 0 1k x u x t dx e t email protected email protected t which is called the boundary integral overspecification the main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known adomian decomposition method the decomposition procedure of adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form furthermore due to the rapid convergence of adomian s method a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution this method provides a reliable algorithm that requires less work if compared with the traditional techniques some illustrative examples are presented to show the efficiency of the presented method

application of sinc collocation method for solving an inverse problem in this article the identification of an unknown time dependent source term in an inverse problem of parabolic type with nonlocal boundary conditions is considered the main approach is to change the inverse problem to a system of volterra integral equations the resulting integral equations are convolution type which by using sinc collocation method are replaced by a system of linear algebraic equations the convergence analysis is included and it is shown that the error in the approximate solution is bounded in the infinity norm by the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system to show the efficiency of the present method an example is presented the method is easy to implement and yields very accurate results

the detection and estimation of long memory in stochastic volatility abstract we propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility lmsv model the lmsv model is constructed by incorporating an arfima process in a standard stochastic volatility scheme strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the gaussian likelihood the finite sample properties of the spectral likelihood estimator are analyzed by means of a monte carlo study an empirical example with a long time series of stock prices demonstrates the superiority of the lmsv model over existing short memory volatility models

note on the kth laplacian eigenvalues of trees with perfect matchings abstract denote by k t the k th laplacian eigenvalue of tree t let t n be the set of all trees of order n with perfect matchings in this paper we characterize the tree t in t 4 t with 2 t t 2 t 2 4 2 and the tree in t 6 t with 3 t t 2 t 2 4 2 these results affirm problem of j x li w c shiu a chang 2010 5 for the cases k 2 and k 3 respectively

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

on the numerical solution of multi dimensional parabolic problem by the additive splitting up method several numerical methods arising from the difference methods for certain classes of two dimensional parabolic equation are based on an operator slitting from the theoretical point of view the success and the evaluation of the splitting approach is primarily determined by the accuracy and the stability constrained most of the splitting methods defined in the past decades were of multiplicative non parallel types with respect to the spatial variables in 1994 lui tai and neittaanmaki presented a parallelisable implicit splitting type of methods of different order of approximation and its of additive type with regard to the solution at the advanced time step in this paper the stability analysis will be presented for the implicit splitting methods by lu et al and also we presented a parallelisable explicit splitting algorithm several model problems are solved by the splitting up algorithms to enhance the theoretical results and the concluding remarks

on series representations for linear predictors the series expressions for the linear predictors of a stationary process have been known for a long time but necessary and sufficient conditions for the mean square convergence of these series are still not available it is shown that an equivalent problem is to find necessary and sufficient conditions for the invertibility of the infinite moving average representation of the process two known sufficient conditions are discussed and a more general condition that includes both as special cases is given the process that arises from fractional differencing of a random walk is discussed as an example

numerical solution of the higher order linear fredholm integro differential difference equation with variable coefficients the main aim of this paper is to apply the legendre polynomials for the solution of the linear fredholm integro differential difference equation of high order this equation is usually difficult to solve analytically our approach consists of reducing the problem to a set of linear equations by expanding the approximate solution in terms of shifted legendre polynomials with unknown coefficients the operational matrices of delay and derivative together with the tau method are then utilized to evaluate the unknown coefficients of shifted legendre polynomials illustrative examples are included to demonstrate the validity and applicability of the presented technique and a comparison is made with existing results

a new modification of the adomian decomposition method for linear and nonlinear operators in this paper we present an efficient modification of the adomian decomposition method that will facilitate the calculations we then conduct a comparative study between the new modification and the modified decomposition method the study is conducted through illustrative examples the new modification introduces a promising tool for many linear and nonlinear models

chebyshev polynomials approach for numerically solving system of two dimensional fractional pdes and convergence analysis abstract in this paper an efficient numerical technique based on the chebsyhev orthogonal polynomials is established to obtain the approximate solutions of system of two dimensional fractional order pdes with initial conditions we construct the corresponding differential operational matrix of fractional order and then transform the problem into a system of linear algebra equations compared with other analytical or semi analytical methods ours can achieve better convergence accuracy only small terms are expanded moreover the proposed algorithm is simple in theoretical derivation and numerical simulation in our study the convergence analysis of the system is emphatically investigated than other numerical approaches lastly three numerical examples are applied to test the algorithm and that the obtained numerical results show that our approach is effective and robust

approximate solutions to boundary value problems of higher order by the modified decomposition method abstract in this paper we present an efficient numerical algorithm for approximate solutions of higher order boundary value problems with two point boundary conditions a modified form of the adomian decomposition method will be implemented to construct such solutions the approach provides the solution in the form of a rapidly convergent series the analysis is accompanied by numerical examples the obtained results demonstrate reliability and efficiency of the proposed scheme

a consistent nonparametric test of ergodicity for time series with applications we propose a set of algorithms for testing the ergodicity of empirical time series without reliance on a specific parametric framework it is shown that the resulting test asymptotically obtains the correct size for stationary and nonstationary processes and maximal power against non ergodic but stationary alternatives the test will not reject in the presence of nonstationarity that does not lead to ergodic failure the method is used to investigate debates over stability of monetary aggregates relative to gdp and the mean reversion hypothesis with respect to high frequency data on exchange rates both the monte carlo and data analysis results suggest that the test has good size and power performance

on the second order implicit difference schemes for a right hand side identification problem in many physical phenomena especially in temperature over specification partial differential equation with an unknown source function appears the present paper is devoted to the study of the well posedness of the approximate solution of a right hand side identification problem for a parabolic equation the second order of accuracy implicit difference scheme is presented the coercive stability estimates for the solution of this difference scheme are obtained the theoretical statements for the solution of this difference schemes are supported by results of numerical experiments

analysis of a time domain finite element method for 3 d maxwell s equations in dispersive media abstract we consider the time dependent maxwell s equations in dispersive media on a bounded domain in three dimensional space a fully discrete finite element scheme is developed to approximate the electric field equation derived from the maxwell s equations optimal energy norm error estimates are proved for nedelec curl conforming edge elements this is the first finite element error analysis for maxwell s equations in dispersive media

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

a class of non linear non classical parabolic equations abstract in this paper we deal with a class of non classical parabolic equations which arise from some practical problems such as the identification of unknown parameters free boundary problems etc one of the characteristics of this kind of equation is that the maximum principle is no longer valid we will first study the local solvability for a general equation of this kind via an auxiliary problem and the schauder fixed point principle then some a priori estimates are derived to establish the global existence of the solution moreover uniqueness and continuous dependence of the solution are proved finally some examples are given to illustrate the applications of the theory

a reliable technique for solving the weakly singular second kind volterra type integral equations abstract in this paper the adomian decomposition method and the phenomenon of the self canceling noise terms are used for solving the weakly singular volterra type linear and nonlinear integral equations the solution obtained is in the form of a convergent power series with elegantly computable terms comparing this scheme with many collocation type methods that use the nonpolynomial basis shows that the present approach is effective and powerful many test modeling problems from mathematical physics linear and nonlinear are discussed to illustrate the effectiveness and the performance of the decomposition method

inference in arch and garch models with heavy tailed errors arch and garch models directly address the dependency of conditional second moments and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present these include financial time series which can be particularly heavy tailed however little is known about properties of arch or garch models in the heavy tailed setting and no methods are available for approximating the distributions of parameter estimators there in this paper we show that for heavy tailed errors the asymptotic distributions of quasi maximum likelihood parameter estimators in arch and garch models are nonnormal and are particularly difficult to estimate directly using standard parametric methods standard bootstrap methods also fail to produce consistent estimators to overcome these problems we develop percentile t subsample bootstrap approximations to estimator distributions studentizing is employed to approximate scale and the subsample bootstrap is used to estimate shape the good performance of this approach is demonstrated both theoretically and numerically

numerical solution of one dimensional parabolic inverse problem this paper is concerned with numerical techniques for the solution of a one dimensional parabolic inverse problem with a control parameter the discrete approximation of the problem is based on the finite difference schemes these techniques are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain the main idea behind the finite difference methods for obtaining the solution of a given partial differential equation is to approximate the derivatives appearing in the equation by a set of values of the function at a selected number of points the most usual way to generate these approximations is through the use of taylor series the methods developed here are based on the modified equivalent partial differential equation as described by warming and hyett j comput phys 14 2 1974 159 this approach allows the simple determination of the theoretical order of accuracy thus allowing methods to be compared with one another also from the truncation error of the modified equivalent equation it is possible to eliminate the dominant error terms associated with the finite difference equations that contain free parameters weights thus leading to more accurate methods the results of a numerical experiment are presented and accuracy and the central processor cpu time needed for the parabolic inverse problem are discussed

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

inversion theory for parameterized diffusion problem invertibility is established for the mathematical formulation most often used to describe the one dimensional magnetotelluric problem and related nondestructive testing techniques using the terminology of the applications for a large space of conductivity functions with no analyticity requirements recovery of the conductivity function from magnetotelluric data is shown to be unique

proof of a problem on laplacian eigenvalues of trees abstract denote by k l t the k th laplacian eigenvalue of a tree t let t k 2 t be the set of all trees of order 2 t k with perfect matchings in this note the trees t in t k 2 t with k l t t 2 t 2 4 2 are characterized which solves problem of j x li w c shiu and a chang in 3 completely

a tau method for the one dimensional parabolic inverse problem subject to temperature overspecification in this work an approximational technique based on shifted legendre tau ideas is presented for the one dimensional parabolic inverse problem with a control parameter the method consists of expanding the required approximate solution as the elements of a shifted legendre polynomial using the operational matrices we reduce the problem to a set of algebraic equations a numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results the method is easy to implement and produces very accurate results

numerical techniques for a parabolic equation subject to an overspecified boundary condition an inverse problem concerning diffusion equation with a control parameter is considered a new numerical scheme is developed for obtaining approximate solutions to an initial boundary value problem for the semi linear parabolic partial differential equation subject to an overspecified boundary condition the space derivative in the pde is approximated by finite difference replacements the solution of the resulting system of first order ordinary differential equations odes satisfies a recurrence relation which involves a matrix exponential function the accuracy in time can be controlled by choosing several pade approximants to replace this matrix exponential term a numerical technique is developed to compute the required solution using a splitting method leading to algorithms for sequential and parallel implementation the algorithms are tested on a model problem from the literature the results of a numerical experiment are presented and the accuracy and central processor cpu time needed for this inverse problem are discussed

a finite difference method for a non local boundary value problem for two dimensional heat equation a second order finite difference scheme is given for the numerical solution of a two dimensional non local boundary value problem for heat equation using a suitable transformation the solution of this problem is equivalent to the solution of two other problems the first problem which is a one dimensional non local boundary value problem giving the value of m through using a second order finite difference scheme using this result the second problem will be changed to a classical two dimensional problem with nuemann s boundary condition which will be solved numerically the stability properties and truncation error of the new method are discussed and the results of numerical experiments are presented

an inverse problem of identifying the control function in two and three dimensional parabolic equations through the spectral meshless radial point interpolation abstract this study proposes a kind of spectral meshless radial point interpolation smrpi for solving two and three dimensional parabolic inverse problems on regular and irregular domains the smrpi is developed for identifying the control parameter which satisfies the semilinear time dependent two and three dimensional diffusion equation with both integral overspecialization and overspecialization at a point in the spatial domain this method is based on a combination of meshless methods and spectral collocation techniques the point interpolation method with the help of radial basis functions are used to construct shape functions which act as basis functions in the frame of smrpi it is proved that the scheme is stable with respect to the time variable in h1 and convergent by the order of convergence o t the results of numerical experiments are compared to analytical solutions to confirm the accuracy and efficiency of the presented scheme

a tau approach for solution of the space fractional diffusion equation fractional differentials provide more accurate models of systems under consideration in this paper approximation techniques based on the shifted legendre tau idea are presented to solve a class of initial boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain the fractional derivatives are described in the caputo sense the technique is derived by expanding the required approximate solution as the elements of shifted legendre polynomials using the operational matrix of the fractional derivative the problem can be reduced to a set of linear algebraic equations from the computational point of view the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use

diffusion subject to the specification of mass abstract existence uniqueness and continuous dependence upon the data are demonstrated for the solution u u x t of the diffusion equation ut uxx s x t 0 u x 0 x 0 ux 1 t g t 0 0 b 0 x dx m 0 a numerical procedure is discussed and results of numerical experiments are presented

direct meshless local petrov galerkin dmlpg method for time fractional fourth order reaction diffusion problem on complex domains abstract a new numerical scheme has been developed based on the fast and efficient meshless local weak form i e direct meshless local petrov galerkin dmlpg method for solving the fractional fourth order partial differential equation on computational domains with complex shape the fractional derivative is the riemann liouville fractional derivative at first a finite difference scheme with the second order accuracy has been employed to discrete the time variable then the dmlpg technique is employed to achieve a full discrete scheme the time discrete scheme has been studied in terms of unconditional stability and convergence order by the energy method in the l 2 space also some numerical results are presented to show the efficiency and accuracy of the proposed technique on the simple and complex domains with the irregular and non regular grid points

identifying a control function in two dimensional parabolic inverse problems numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications this study presents numerical schemes for solving two two dimensional parabolic inverse problems i e for the determination of some unknown functions in the parabolic partial differential equations these schemes are developed for determining the parameter p t which satisfy u t u x x u y y p t email protected in rx 0 t u x y 0 f x y x y r 0 1 2 it is assumed that u is known on the boundary of r and subject to the integral overspecification over a portion of the spatial domain 0 email protected 0 1u x y t dxdy e t 0

fracture analysis in continuously nonhomogeneous magneto electro elastic solids under a thermal load by the mlpg abstract a meshless method based on the local petrov galerkin approach is proposed to solve initial boundary value problems of magneto electro elastic solids with continuously varying material properties stationary and transient thermal problems are considered in this paper the mechanical 2 d fields are described by the equations of motion with an inertial term nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity the spatial variation of displacements electric and magnetic potentials is approximated by the moving least squares mls scheme after performing the spatial integrations one obtains a system of ordinary differential equations for certain nodal unknowns that system is solved numerically by the houbolt finite difference scheme as a time stepping method

identification of time dependent source terms and control parameters in parabolic equations from overspecified boundary data abstract this paper presents a semigroup approach for inverse source problems for the abstract heat equation when the measured output data is given in subject to the integral overspecification over the spatial domain the existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed such representation permits the derivation of sufficient conditions for the uniqueness of the solution also an approximation method based on the optimal homotopy analysis method oham is designed and the error estimates are discussed using graphical analysis moreover we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data the proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations the accuracy and stability of the method are discussed and compared with several finite difference techniques computational results show efficiency and high accuracy of the proposed algorithm

a meshless local petrov galerkin method for the time dependent maxwell equations abstract in this paper the meshless local petrov galerkin mlpg method is employed to solve the 2 d time dependent maxwell equations the mlpg method is a truly meshless method in which the trial and test functions are chosen from totally different functional spaces in the current work the moving least square reproducing kernel mlsrk scheme is chosen to be the trial function the method is applied for the unsteady maxwell equations in different media in the local weak form by employing the difference operator for evolution in time and simultaneously in time and space the semi discrete and fully discrete schemes are obtained respectively the error estimation is discussed for both the semi discrete and fully discrete numerical schemes for modelling the time dependent maxwell equations we show that provided that the time step size is sufficiently small the proposed scheme yields an error of o 2 m 1 2 in the l 2 norm for the square of error the new scheme is implemented and the numerical results are provided to justify our theoretical analysis

existence and uniqueness properties for the one dimensional magnetotellurics inversion problem the one dimensional magnetotelluric mt inversion problem is well known to be ill posed and nonlinear this paper seeks an understanding of the mappings underlying the nonlinear relationships these properties are used to study the validity of some exploration aspects of the problem that are essential for the practical use of mt as an exploration tool this study has two major segments results in response space and results in geologic space in response space the existence of optimal admittance curves has been proven in the case of continuous data uniqueness has been established for discrete data a relationship between alternative optimal solutions has been derived in geologic space the results are extremely significant to mt s applicability to exploration a class of conductivity functions y which contains all possible natural geological conditions has been used as a framework for the study over this class y the one dimensional magnetotellurics problem has been proven to be uniquely invertible from the admittance curves this precludes the possibility of two different geologic models yielding the same complete data as a result the path is now clear to generate a description of a unimodal statistical distribution of feasible inversions to the real world exploration problem with finitely sampled noisy data

theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes abstract here we present a theoretical study on the main properties of fractionally integrated exponential generalized autoregressive conditional heteroskedastic fiegarch processes we analyze the conditions for the existence the invertibility the stationarity and the ergodicity of these processes we prove that if x t t z is a fiegarch p d q process then under mild conditions ln x t 2 t z is an arfima q d 0 with correlated innovations that is an autoregressive fractionally integrated moving average process the convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes ln x t 2 t z and ln t 2 t z are discussed expressions for the kurtosis and the asymmetry measures for any stationary fiegarch p d q process are also derived the h step ahead forecast for the processes x t t z ln t 2 t z and ln x t 2 t z are given with their respective mean square error of forecast the work also presents a monte carlo simulation study showing how to generate estimate and forecast based on six different fiegarch models the forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models namely arch type models and radial basis models is compared through an empirical application to brazilian stock market exchange index