numerical methods for the solution of special and general sixth order boundary value problems with applications to benard layer eigenvalue problems a family of numerical methods is developed for the solution of special nonlinear sixth order boundary value problems methods with second fourth sixth and eighth order convergence are contained in the family the problem is also solved by writing the sixth order differential equation as a system of three second order differential equations a family of second and fourth order convergent methods is then used to obtain the solution a second order convergent method is discussed for the numerical solution of general nonlinear sixth order boundary value problems this method with modifications where necessary is applied to the sixth order eigenvalue problems associated with the onset of instability in a benard layer numerical results are compared with asymptotic estimates appearing in the literature

poincare group and relativistic wave equations in dimensions using the generalized regular representation an explicit construction of the unitary irreducible representations of the 2 1 poincare group is presented a detailed description of the angular momentum and spin in 2 1 dimensions is given on this base the relativistic wave equations for all spins including fractional are constructed

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

a modification of the adomian decomposition method for a class of nonlinear singular boundary value problems in this paper the adomian decomposition method is modified to solve a class of nonlinear singular boundary value problems which arise as nonlinear normal modal equations in nonlinear conservative vibratory systems the effectiveness of the modified method is verified by three examples

the modified decomposition method for eighth order boundary value problems a modified adomian decomposition method is developed for the numerical solution of eighth order boundary value problems bvps the calculated numerical results show reliability and efficiency of the algorithm given the numerical procedure is tested on linear and nonlinear problems

the solution of multipoint boundary value problems by the optimal homotopy asymptotic method in this work we solve multipoint boundary value problems using the optimal homotopy asymptotic method oham the proposed method is tested upon several problems from the literature and the results are compared with the available exact solution this method provides easy tools to control the convergence region of approximating solution series where ever necessary

parametric septic splines approach for the solution of linear sixth order two point boundary value problems parametric splines which reduces to seven degree polynomial splines have been used to develop a class of numerical methods for the solution of linear sixth order two point boundary value problems convergence analysis of the methods is discussed through standard procedure it is shown that the present methods give approximations which are better than those produced by other splines and domain decomposition methods three numerical examples are given to illustrate the practical usefulness of the new approach

homotopy perturbation method for solving sixth order boundary value problems in this paper we apply the homotopy perturbation method for solving the sixth order boundary value problems by reformulating them as an equivalent system of integral equations this equivalent formulation is obtained by using a suitable transformation the analytical results of the integral equations have been obtained in terms of convergent series with easily computable components several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method comparisons are made to confirm the reliability of the homotopy perturbation method we have also considered an example where the homotopy perturbation method is not reliable

two approaches based on pole sensitivity and stability radius measures for finite precision digital controller realizations this paper compares the two approaches based on pole sensitivity and the complex stability radius measures respectively for optimizing the closed loop stability robustness of digital controllers with respect to finite word length fwl errors in fixed point implementation design details and related optimization procedures are derived for the two methods the two measures although derived from different motivations can both be regarded as lower bound measures of a true but computationally intractable fwl stability measure in some senses an example is used to verify the theoretical analysis and to illustrate the two designs for determining optimal fwl controller realizations

relativistic field theories in three dimensions we provide a complete classification of the unitary irreducible representations of the 2 1 dimensional poincare group we show in particular that only two types of spin are available for massless field theories we also construct generalized foldy wouthuysen transformations which connect the physical uir s with covariant field theories in three dimensions

septic spline solutions of sixth order boundary value problems septic spline is used for the numerical solution of the sixth order linear special case boundary value problem end conditions for the definition of septic spline are derived consistent with the sixth order boundary value problem the algorithm developed approximates the solution and their higher order derivatives the method has also been proved to be second order convergent three examples are considered for the numerical illustrations of the method developed the method developed in this paper is also compared with that developed in m el gamel j r cannon j latour a i zayed sinc galerkin method for solving linear sixth order boundary value problems mathematics of computation 73 247 2003 1325 1343 as well and is observed to be better

the sinc galerkin method for fourth order differential equations the sinc galerkin method originally proposed by stenger is extended to handle fourth order ordinary differential equations the exponential convergence rate of the method o e kappa sqrt m is carefully developed and the special features of the discrete system are described spectral properties and conditioning of the associated matrices are given the appropriate choice of weight function in the galerkin inner product is discussed with primary emphasis given to choices that are best suited to fourth order partial differential equations numerical results are included to help illustrate the parameter selections made and confirm the efficiency and accuracy of the method

variational approach to the sixth order boundary value problems recently wazwaz appl math comput 118 2001 311 325 applied the adomian s decomposition method to solve analytically the solution of sixth order boundary value problems the same problem is discussed via the variational principle which reveals to be much more simpler and much more efficient

sinc galerkin method for solving linear sixth order boundary value problems mmthere are few techniques available to numerically solve sixth order boundary value problems with two point boundary conditions in this paper we show that the sinc galerkin method is a very effective tool in numerically solving such problems the method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made it is shown that the sinc galerkin method yields better results

pseudospherical functions on a hyperboloid of one sheet the pseudospherical functions on one sheet two dimensional hyperboloid are discussed the simplest method of construction of these functions is introduced using the fock space structure of the representation space of the su 1 1 algebra the pseudospherical functions with half integer order are investigated the counterparts of the legendre functions for the hyperboloid are introduced and a new class of pseudospherical functions is found

comparative study on optimizing closed loop stability bounds of finite precision controller structures with shift and delta operators the paper analyzes the sensitivity of closed loop stability with respect to w r t finite word length fwl effects in the implementation of the controller coefficients using both the shift and delta operator parameterizations a unified approach is established to optimize a closed loop stability lower bound for fwl controller structures this provides a general framework to compare the fwl closed loop stability characteristics of the controller structures based on the shift and delta operators respectively two numerical examples are given and the simulation results show that the optimal fwl controller realizations with the delta operator have better closed loop stability margins than those with the shift operator

coherent states of su l 1 groups this work can be considered as a continuation of our previous study in which an explicit form of coherent states cs for all su n groups was constructed by means of representations on polynomials here we extend that approach to any su l 1 group and construct explicitly corresponding cs the cs are parametrized by dots of a coset space which is in that particular case the open complex ball cdl this space together with the projective space cpl which parametrizes the cs of the su l 1 group exhaust all complex spaces of constant curvature thus both sets of cs provide a possibility for an explicit analysis of the quantization problem on all the spaces of constant curvature this is why the cs of the su n and su l 1 groups are of importance in connection with quantization theory the constructed cs form an overcompleted system in the representation space and as quantum states possessing a minimum uncertainty they minimize an invariant dispersion of the quadratic casimir operator the classical limit is investigated in terms of symbols of operators the limit of the so called star commutator of the symbols generates the poisson bracket in cdl the latter plays the role of the phase space for the corresponding classical mechanics

a new algorithm for solving classical blasius equation in this paper a reliable algorithm is employed to investigate the classical blasius equation the algorithm is based mainly on applying the adomian decomposition method to the transformation of the blasius equation the results demonstrate reliability and efficiency of the proposed algorithm

the unitary irreducible representations of sl 2 r in all subgroup reductions we use the canonical transform realization of sl 2 r in order to find all matrix elements and integral kernels for the unitary irreducible representations of this group explicit results are given for all mixed bases and subgroup reductions these provide the full multiparameter set of integral transforms and series expansions associated to sl 2 r

optimizing stability bounds of finite precision pid controller structures this paper investigates a recently derived lower bound stability measure for sampled data controller structures subject to finite wordlength fwl constraints the optimal realization of the digital pid controller with fwl considerations is formulated as a nonlinear optimization problem and an efficient strategy based on adaptive simulated annealing asa is adopted to solve this complex optimization problem a numerical example of optimizing the finite precision pid controller structure for a simulated steel rolling mill system is presented to illustrate the effectiveness of the proposed strategy

optimal realisations of fixed point implemented digital controller with the smallest dynamic range a novel approach is proposed to design optimal finite word length fwl realizations of digital controllers implemented in fixed point arithmetic a minimax based search procedure is first formulated to obtain an optimal controller realization that optimizes an fwl closed loop stability measure since this fwl closed loop stability measure is solely linked to the fractional part or precision of fixed point format the resulting realization may not have the smallest dynamic range a measure is then derived to indicate the dynamic range of fixed point implemented realization by choosing an appropriate orthogonal transformation of this dynamic range measure of the optimal precision controller realization a numerical optimization method is developed to make the controller realization having the smallest dynamic range without sacrificing fwl closed loop stability robustness the proposed approach is more efficient than a direct optimization of some combined fwl closed loop stability and dynamic range measure

a comparison between the sinc galerkin and the modified decomposition methods for solving two point boundary value problems one of the new techniques used in solving boundary value problems involving ordinary differential equations is the sinc galerkin method this method has been shown to be a powerful numerical tool for finding fast and accurate solutions a less known technique that has been around for almost two decades is the decomposition method in this paper we solve boundary value problems of higher order using these two methods and then compare the results it is shown that the sinc galerkin method in many instances gives better results

non polynomial splines approach to the solution of sixth order boundary value problems non polynomial splines which are equivalent to seven degree polynomial splines are used to develop a class of numerical methods for computing approximations to the solution of sixth order boundary value problems with two point boundary conditions second fourth and sixth order convergence is obtained by using standard procedure it is shown that the present methods give approximations which are better than those produced by other spline and domain decomposition methods numerical examples are given to illustrate practical usefulness of the new approach

adomian decomposition method with green s function for sixth order boundary value problems in this paper the adomian decomposition method with green s function is applied to solve linear and nonlinear sixth order boundary value problems the numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the decomposition method is of high accuracy more convenient and efficient for solving high order boundary value problems

symmetrization of the sinc galerkin method for boundary value problems on procede a la symetrisation de la methode de galerkin en modifiant la fonction poids pour une classe etendue de problemes aux valeurs limites

optimal finite precision state estimate feedback controller realizations of discrete time systems investigates the stability issue of a discrete time control system where a state estimate feedback controller sefc digitally implemented with a fixed point format is used a tractable closed loop stability related measure is derived with finite word length implementation consideration of the controller the optimal realizations of the sefc are defined as those that maximize this measure and can be shown as the solutions of a nonlinear programming problem a sophisticated optimization strategy is presented to provide an efficient method for solving this problem and a numerical example is given to illustrate the design procedure

a new convergence proof of the adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws in this paper we propose a new convergence proof of the adomian s decomposition method adm applied to the generalized nonlinear system of partial differential equations pde s based on new formula for adomian polynomials the decomposition scheme obtained from the adm yields an analytical solution in the form of a rapidly convergent series for a system of conservation laws systems of conservation laws is presented we obtain the stability of the approximate solution when the system changes type we show with an explicit example that the latter property is true for general cauchy problem satisfying convergence hypothesis the results indicate that the adm is effective and promising

the numerical solution of sixth order boundary value problems by the modified decomposition method a fast and accurate algorithm is developed for the solution of sixth order boundary value problems bvps with two point boundary conditions a modified form of the adomian decomposition method is applied to construct the numerical solution for such problems the scheme is tested on one linear and two nonlinear problems the results demonstrate reliability and efficiency of the algorithm developed

an improved closed loop stability related measure for finite precision digital controller realizations the pole sensitivity approach is employed to investigate the stability issue of the discrete time control system where a digital controller implemented with finite word length fwl is used a stability related measure is derived which is more accurate in estimating the closed loop stability robustness of an fwl implemented controller than some existing measures for the pole sensitivity analysis this improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output feedback and observer based controllers a numerical example is used to verify the theoretical analysis and to illustrate the design procedure

an algorithm for adomian decomposition method in this paper a reliable technique for calculating adomian polynomials for nonlinear operators is developed the algorithm is fulfilled with symbolic computation so that the adomian decomposition methods for solving differential equations can be mechanized in maple ten examples are presented to illustrate the implementation of the program

convergence of adomian s decomposition method periodic temperatures abstract the convergence of adomian s decomposition method 1 as applied to periodic temperature fields in heat conductors is investigated

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

on the structure of digital controllers with finite word length consideration it is well known that a stable discrete time control system may become unstable when the digital controller is actually implemented with a digital control processor due to the finite word length effects and that the stability behavior of the system depends on the structure of the digital controller due to the difficulties in adopting the existing stability robustness measures a new measure is derived which is tractable and hence enables us to handle the digital controller structure problem easily the optimal controller structure problem is formulated by maximizing this measure an analytical solution is presented an algorithm is developed for finding sparser structures

a new modification of the adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations abstract in this paper we propose a new modified recursion scheme for the resolution of multi order and multi point boundary value problems for nonlinear ordinary and partial differential equations by the adomian decomposition method adm our new approach including duan s convergence parameter provides a significant computational advantage by allowing for the acceleration of convergence and expansion of the interval of convergence during calculations of the solution components for nonlinear boundary value problems in particular for such cases when one of the boundary points lies outside the interval of convergence of the usual decomposition series we utilize the boundary conditions to derive an integral equation before establishing the recursion scheme for the solution components thus we can derive a modified recursion scheme without any undetermined coefficients when computing successive solution components whereas several prior recursion schemes have done so this modification also avoids solving a sequence of nonlinear algebraic equations for the undetermined coefficients fraught with multiple roots which is required to complete calculation of the solution by several prior modified recursion schemes using the adm

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

quintic spline solution of linear sixth order boundary value problems abstract there are few techniques available to numerically solve sixth order boundary value problems with two point boundary conditions in this paper quintic spline method is developed for the numerical solutions of linear special case sixth order boundary value problems two examples are considered for the numerical illustration of the method developed the method is also compared with those developed by el gamel et al mohamed el gamel john r cannon ahmed i zayed sinc galerkin method for solving sixth order bvps math comput 73 247 2003 and wazwaz a wazwaz the numerical solution of sixth order boundary value problems by the modified decomposition method appl math comput 118 2001 311 325 the comparison shows that the quintic spline method is more efficient and effective tool and yields better results

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

sinc numerical solution for solitons and solitary waves abstract a numerical scheme using sinc galerkin method is developed to approximate the solution for the korteweg de vries model equation sinc approximation to both derivatives and indefinite integral reduce the integral equation to an explicit system of algebraic equations then using various properties of sinc functions it is shown that the sinc solution produce an error of order o exp c h for some positive constants c h the method is applied to a few test examples to illustrate the accuracy and the implementation of the method

a µ based optimal finite word length controller design a novel optimal finite word length fwl controller design is proposed in the framework of m theory a computationally tractable close loop stability measure with fwl implementation considerations of the controller is derived based on the m theory and the optimal fwl controller realizations are obtained by solving the resulting optimal fwl realization problem using linear matrix inequality techniques

b spline collocation for solution of two point boundary value problems a numerical method based on b spline is developed to solve the general nonlinear two point boundary value problems up to order 6 the standard formulation of sextic spline for the solution of boundary value problems leads to non optimal approximations in order to derive higher orders of accuracy high order perturbations of the problem are generated and applied to construct the numerical algorithm the error analysis and convergence properties of the method are studied via green s function approach o h 6 global error estimates are obtained for numerical solution of these classes of problems numerical results are given to illustrate the efficiency of the proposed method results of numerical experiments verify the theoretical behavior of the orders of convergence