solution of boundary value problems for integro differential equations by using differential transform method in this study we extended the differential transform method dtm to solve the integro differential equations new theorems for the transformation of integrals are introduced and prooved the commonly encountered linear and nonlinear integro differential equations that appear in literature are solved as an illustration for the efficiency of the method some numerical results are also given to demonstrate the superiority of the method to other common techniques the results we obtained by using this technique is much more accurate compared to the existing ones

high order nonlinear initial value problems countably determined we give a numerical approximation of the solution of a high order nonlinear initial value problem by making use of certain properties of an adequate schauder basis

new approaches to robust minimum variance filter design this paper is concerned with the design of robust filters that ensure minimum filtering error variance bounds for discrete time systems with parametric uncertainty residing in a polytope two efficient methods for robust kalman filter design are introduced the first utilizes a recently introduced relaxation of the quadratic stability requirement of the stationary filter design the second applies the new method of recursively solving a semidefinite program sdp subject to linear matrix inequalities lmis constraints to obtain a robust finite horizon time varying filter the proposed design techniques are compared with other existing methods it is shown via two examples that the results obtained by the new methods outperform all of the other designs

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

applications of differential transform method to differential algebraic equations in this paper numerical solution of linear differential algebraic equations daes is considered by differential transform method two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions differential transform method can easily be applied to daes and series solutions are obtained after the transformation here we have formulated series coefficients very simply for the considered problems

numerical solution of three dimensional volterra fredholm integral equations of the first and second kinds based on bernstein s approximation abstract a new and efficient method is presented for solving three dimensional volterra fredholm integral equations of the second kind 3d vfiek2 first kind 3d vfiek1 and even singular type of these equations here we discuss three variable bernstein polynomials and their properties this method has several advantages in reducing computational burden with good degree of accuracy furthermore we obtain an error bound for this method finally this method is applied to five examples to illustrate the accuracy and implementation of the method and this method is compared to already present methods numerical results show that the new method provides more efficient results in comparison with other methods

an iterative multistep kernel based method for nonlinear volterra integral and integro differential equations of fractional order abstract an iterative multistep kernel based method is proposed for the nonlinear volterra integral equations and nonlinear volterra integro differential equations of fractional order which can produce reliable globally smooth numerical solutions an error estimate of the positive definite kernel interpolation and the convergence and error analysis of the proposed iterative scheme are investigated here we focused on positive definite radial basis kernels and further a new and applicable shape parameter selection strategy is proposed the proposed multi step method set up and solve several small local problems instead of a single large problem which makes it suitable for problems with long time simulations in order to show the efficiency and versatility of the proposed method some numerical experiments are reported the comparison of the numerical results with the analytical solutions and the best reported results in the literature confirm the good accuracy and applicability of the proposed method

extrapolation of nystrom solution for two dimensional nonlinear fredholm integral equations abstract in this paper we analyze the existence of asymptotic error expansion of the nystrom solution for two dimensional nonlinear fredholm integral equations of the second kind we show that the nystrom solution admits an error expansion in powers of the step size h and the step size k for a special choice of the numerical quadrature the leading terms in the error expansion for the nystrom solution contain only even powers of h and k beginning with terms h2p and k2q these expansions are useful for the application of richardson extrapolation and for obtaining sharper error bounds numerical examples show that how richardson extrapolation gives a remarkable increase of precision in addition to faster convergence

online adaptive optimal control for continuous time nonlinear systems with completely unknown dynamics an online adaptive optimal control is proposed for continuous time nonlinear systems with completely unknown dynamics which is achieved by developing a novel identifier critic based approximate dynamic programming algorithm with a dual neural network nn approximation structure first an adaptive nn identifier is designed to obviate the requirement of complete knowledge of system dynamics and a critic nn is employed to approximate the optimal value function then the optimal control law is computed based on the information from the identifier nn and the critic nn so that the actor nn is not needed in particular a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier nn and critic nn simultaneously which converge to small neighbourhoods around their ideal values the closed loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the lyapunov theory the proposed ada

solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method in this paper we will give some results for developing the two dimensional differential transform tddt for double integrals then the tddt method will be developed for solving a class of two dimensional linear and nonlinear volterra integral equations we also give some examples to demonstrate the accuracy of the method

a computational method for solving a class of two dimensional volterra integral equations the use of the geometric series theorem together with schauder bases in certain banach spaces allows us to design a numerical algorithm in order to solve an important type of two dimensional linear integral equations a study of the convergence and error is presented here all the calculations can be easily implemented and the efficiency of this method will be shown with numerical results

performance of map reconstruction for hot lesion detection in whole body pet ct an evaluation with human and numerical observers for positron emission tomography pet imaging different reconstruction methods can be applied including maximum likelihood ml and maximum a posteriori map reconstruction postsmoothed ml images have approximately position and object independent spatial resolution which is advantageous for semi quantitative analysis however the complex object dependent smoothing obtained with map might yield improved noise characteristics beneficial for lesion detection in this contribution map and postsmoothed ml are compared for hot spot detection by human observers and by the channelized hotelling observer cho the study design was based on the ldquomultiple alternative forced choicerdquo approach for the map reconstruction the relative difference prior was used for postsmoothed ml a gaussian smoothing kernel was used both the human observers and the cho performed slightly better on map images than on postsmoothed ml images the average cho performance was similar to the best human performance the cho was then applied to evaluate the performance of priors with reduced penalty for large differences for these priors a poorer detection performance was obtained

finite horizon robust kalman filter design we study the problem of finite horizon kalman filtering for systems involving a norm bounded uncertain block a new technique is presented for robust kalman filter design this technique involves using multiple scaling parameters that ran be optimized by solving a semidefinite program the use of optimized scaling parameters leads to an improved design a recursive design method that can be applied to real time applications is also proposed

an algorithm based on q i modified splines for singular integral models abstract in this paper we propose an algorithm supporting an approximation using quasi interpolatory q i splines for the numerical solution of integro differential equations with cauchy singular kernel some different choices of parameters defining the numerical model are analyzed and compared in view of the algorithm efficiency

accelerated image reconstruction using ordered subsets of projection data the authors define ordered subset processing for standard algorithms such as expectation maximization em for image restoration from projections ordered subsets methods group projection data into an ordered sequence of subsets or blocks an iteration of ordered subsets em is defined as a single pass through all the subsets in each subset using the current estimate to initialize application of em with that data subset this approach is similar in concept to block kaczmarz methods introduced by eggermont et al 1981 for iterative reconstruction simultaneous iterative reconstruction sirt and multiplicative algebraic reconstruction mart techniques are well known special cases ordered subsets em os em provides a restoration imposing a natural positivity condition and with close links to the em algorithm os em is applicable in both single photon spect and positron emission tomography pet in simulation studies in spect the os em algorithm provides an order of magnitude acceleration over em with restoration quality maintained

steady state kalman filtering with an h error bound abstract an estimator design problem is considered which involves both l 2 least squares and h worst case frequency domain aspects specifically the goal of the problem is to minimize an l 2 state estimation error criterion subject to a prespecified h constraint on the state estimation error the h estimation error constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on the l 2 state estimation error the principal result is a sufficient condition for characterizing fixed order i e full and reduced order estimators with bounded l 2 and h estimation error the sufficient condition involves a system of modified riccati equations coupled by an oblique projection i e idempotent matrix when the h constraint is absent the sufficient condition specializes to the l 2 state estimation result given in 2

neural network observer based optimal control for unknown nonlinear systems using adaptive dynamic programming in this paper an observer based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming adp algorithm first a neural network nn observer is designed to estimate system states then based on the observed states a neuro controller is constructed via adp method to obtain the optimal control in this design two nn structures are used a three layer nn is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics and a critic nn is employed to approximate the value function the optimal control law is computed using the critic nn and the observer nn uniform ultimate boundedness of the closed loop system is guaranteed the actor critic and observer structures are all implemented in real time continuously and simultaneously finally simulation results are presented to demonstrate the effectiveness of the proposed control scheme

quasi interpolatory splines based on schoenberg points by using the schoenberg points as quasi interpolatory points we achieve both generality and economy in contrast to previous sets which achieve either generality or economy but not both the price we pay is a more complicated theory and weaker error bounds although the order of convergence is unchanged applications to numerical integration are given and numerical examples show that the accuracy achieved using the schoenberg points is comparable to that using other sets

a numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions abstract in this paper we use hat basis functions to solve the system of fredholm integral equations sfies and the system of volterra integral equations svies of the second kind this method converts the system of integral equations into a linear or nonlinear system of algebraic equations also we consider the order of convergence of the method and show that it is o h 2 application of the method on some examples show its accuracy and efficiency

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

solutions of the system of differential equations by differential transform method in this study three dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time moreover as an application of two and three dimensional differential transform exact solutions of linear and non linear systems of partial differential equations have been investigated the results of the present method are compared very well with those obtained by decomposition method differential transform method can easily be applied to linear or non linear problems and reduces the size of computational work with this method exact solutions may be obtained without any need of cumbersome work and it is an useful tool for analytical and numerical solutions

numerical solution of linear fredholm integral equations via two dimensional modification of hat functions abstract in this work we approximate the solution of the linear fredholm integral equations by means of a new two dimensional modification of hat functions 2d mhfs and a new operational matrix of integration by this idea the basic equations will be changed into the associated systems of algebraic equations also an error analysis is provided under several mild conditions the method is computationally attractive and some numerical examples are provided to illustrate its high accuracy

solution of the complex modified korteweg de vries equation by the projected differential transform method in this paper we first transform the complex modified korteweg de vries cmkdv equation into a real valued system of partial differential equations then the projected differential transformation method is used to compute an approximate solution of the cmkdv equation three illustrative examples are given to show the effectiveness of the method and comparing with the differential transformation method and the variational iteration method

numerical solution of second kind fredholm integral equations system by using a taylor series expansion method in this paper we present a taylor series expansion method for a second kind fredholm integral equations system with smooth or weakly singular kernels this method reduce the system of integral equations to a linear system of ordinary differential equation after constructing boundary conditions this system reduce to a system of equations that can be solved easily with any of the usual methods finally we show the efficiency of the method using some numerical examples

bounded self weights estimation method for non local means image denoising using minimax estimators a non local means nlm filter is a weighted average of a large number of non local pixels with various image intensity values the nlm filters have been shown to have powerful denoising performance excellent detail preservation by averaging many noisy pixels and using appropriate values for the weights respectively the nlm weights between two different pixels are determined based on the similarities between two patches that surround these pixels and a smoothing parameter another important factor that influences the denoising performance is the self weight values for the same pixel the recently introduced local james stein type center pixel weight estimation method ljs outperforms other existing methods when determining the contribution of the center pixels in the nlm filter however the ljs method may result in excessively large self weight estimates since no upper bound is assumed and the method uses a relatively large local area for estimating the self weights which may lead to a strong bias in this paper we investigated these issues in the ljs method and then propose a novel local self weight estimation methods using direct bounds lmm db and reparametrization lmm rp based on the baranchik s minimax estimator both the lmm db and lmm rp methods were evaluated using a wide range of natural images and a clinical mri image together with the various levels of additive gaussian noise our proposed parameter selection methods yielded an improved bias variance trade off a higher peak signal to noise psnr ratio and fewer visual artifacts when compared with the results of the classical nlm and ljs methods our proposed methods also provide a heuristic way to select a suitable global smoothing parameters that can yield psnr values that are close to the optimal values

differential transform method for the system of two dimensional nonlinear volterra integro differential equations in this paper we develop the differential transform method dtm for solving a class of the system of two dimensional linear and nonlinear volterra integro differential equations of the second kind to this end we give some preliminary results of the differential transform and describe the method of this paper we also give some examples to demonstrate the accuracy of the presented method

nonlocal image and movie denoising neighborhood filters are nonlocal image and movie filters which reduce the noise by averaging similar pixels the first object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other filter classes a ccd noise model will be presented justifying the involvement of neighborhood filters a classification of neighborhood filters will be proposed including classical image and movie denoising methods and discussing further a recently introduced neighborhood filter nl means in order to compare denoising methods three principles will be discussed the first principle method noise specifies that only noise must be removed from an image a second principle will be introduced noise to noise according to which a denoising method must transform a white noise into a white noise contrarily to method noise this principle which characterizes artifact free methods eliminates any subjectivity and can be checked by mathematical arguments and fourier analysis noise to noise will be proven to rule out most denoising methods with the exception of neighborhood filters this is why a third and new comparison principle the statistical optimality is needed and will be introduced to compare the performance of all neighborhood filters the three principles will be applied to compare ten different image and movie denoising methods it will be first shown that only wavelet thresholding methods and nl means give an acceptable method noise second that neighborhood filters are the only ones to satisfy the noise to noise principle third that among them nl means is closest to statistical optimality a particular attention will be paid to the application of the statistical optimality criterion for movie denoising methods it will be pointed out that current movie denoising methods are motion compensated neighborhood filters this amounts to say that they are neighborhood filters and that the ideal neighborhood of a pixel is its trajectory unfortunately the aperture problem makes it impossible to estimate ground true trajectories it will be demonstrated that computing trajectories and restricting the neighborhood to them is harmful for denoising purposes and that space time nl means preserves more movie details

numerical approaches for systems of volterra fredholm integral equations in this work we introduce two numerical methods for solving systems of volterra fredholm integral equations in the nonlinear case we suggest a fixed point method where the iterations are perturbed in a suitable way according to a schauder basis in the banach space of continuous functions c a b 2 in the linear case we propose a collocation method based on a particular class of approximating functions in both methods convergence analysis and or low computational cost are analysed taking into account the properties of the basis under consideration numerical results confirm the theoretical study

reducing the sensitivity to parameter variations of a minimum order reduced order observer a quantitative upper hound is established which defines the extent to which a minimum order reduced order non adaptive observer may be rendered insensitive to parameter variations that upper bound depends on the number of measurements and the location of questionable parameters within the system matrices an integral squared error objective function is explicitly solved that objective function may be used to assess the sensitivity of the system to parameter errors a numerical example is presented for a continuous observer the results are extended to the discrete ease

robust kalman filtering for uncertain systems abstract this paper studies the problem of kalman filter design for uncertain systems the system under consideration is subjected to time varying norm bounded parameter uncertainties in both the state and measurement matrices the problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties a riccati equation approach is proposed to solve the above problem furthermore a suboptimal covariance upper bound can be computed by a convex optimization

product integration of singular integrands using quasi interpolatory splines we consider product integrals of the form kf 11k x f x dx where kf l1 but f is unbounded in the integration interval we shall approximate f by a sequence of quasi interpolatory splines qnf involving only function values and study the convergence of i kqnf to i kf it turns out that we can ignore an endpoint singularity but must in general avoid an interior singularity

postreconstruction nonlocal means filtering of whole body pet with an anatomical prior positron emission tomography pet images usually suffer from poor signal to noise ratio snr due to the high level of noise and low spatial resolution which adversely affect its performance for lesion detection and quantification the complementary information present in high resolution anatomical images from multi modality imaging systems could potentially be used to improve the ability to detect and or quantify lesions however previous methods that use anatomical priors usually require matched organ lesion boundaries in this study we investigated the use of anatomical information to suppress noise in pet images while preserving both quantitative accuracy and the amplitude of prominent signals that do not have corresponding boundaries on computerized tomography ct the proposed approach was realized through a postreconstruction filter based on the nonlocal means nlm filter which reduces noise by computing the weighted average of voxels based on the similarity measurement between patches of voxels within the image anatomical knowledge obtained from ct was incorporated to constrain the similarity measurement within a subset of voxels in contrast to other methods that use anatomical priors the actual number of neighboring voxels and weights used for smoothing were determined from a robust measurement on pet images within the subset thus the proposed approach can be robust to signal mismatches between pet and ct a 3 d search scheme was also investigated for the volumetric pet ct data the proposed anatomically guided median nonlocal means filter amnlm was first evaluated using a computer phantom and a physical phantom to simulate realistic but challenging situations where small lesions are located in homogeneous regions which can be detected on pet but not on ct the proposed method was further assessed with a clinical study of a patient with lung lesions the performance of the proposed method was compared to gaussian edge preserving bilateral and nlm filters as well as median nonlocal means mnlm filtering without an anatomical prior the proposed amnlm method yielded improved lesion contrast and snr compared with other methods even with imperfect anatomical knowledge such as missing lesion boundaries and mismatched organ boundaries

pet image reconstruction using information theoretic anatomical priors we describe a nonparametric framework for incorporating information from co registered anatomical images into positron emission tomographic pet image reconstruction through priors based on information theoretic similarity measures we compare and evaluate the use of mutual information mi and joint entropy je between feature vectors extracted from the anatomical and pet images as priors in pet reconstruction scale space theory provides a framework for the analysis of images at different levels of detail and we use this approach to define feature vectors that emphasize prominent boundaries in the anatomical and functional images and attach less importance to detail and noise that is less likely to be correlated in the two images through simulations that model the best case scenario of perfect agreement between the anatomical and functional images and a more realistic situation with a real magnetic resonance image and a pet phantom that has partial volumes and a smooth variation of intensities we evaluate the performance of mi and je based priors in comparison to a gaussian quadratic prior which does not use any anatomical information we also apply this method to clinical brain scan data using fallypride a tracer that binds to dopamine receptors and therefore localizes mainly in the striatum we present an efficient method of computing these priors and their derivatives based on fast fourier transforms that reduce the complexity of their convolution like expressions our results indicate that while sensitive to initialization and choice of hyperparameters information theoretic priors can reconstruct images with higher contrast and superior quantitation than quadratic priors

observer design methodology for stochastic and deterministic robustness a unified observer with stochastic and deterministic robustness is developed in this paper so that an observer is less sensitive to both stochastic and deterministic uncertainties for stochastic robustness the norm of the observer gain and the lower bound of the observer decay rate are shown to be design factors which can minimize the upper bound of the estimation error variance for deterministic robustness the l 2 norm based condition number of the observer eigenvector matrix is utilized to address robust estimation performance against deterministic uncertainties in order to justify the proposed method a graphical approach is first introduced and then a multi objective optimization problem including linear matrix inequality constraints is formulated to provide the unified robustness

extrapolation method for solving two dimensional volterral integral equations of the second kind abstract in this paper we propose a numerical quadrature method for solving two dimensional linear and nonlinear volterra integral equations firstly we generalize one dimensional quadrature formula to two dimensional case and its corresponding error asymptotic expansion based on the quadrature formula and the error expansion we next construct an iterative scheme and extrapolation algorithm the numerical solution of any point can be calculated by iterative scheme and the error accuracy and convergence order of the numerical solution are further improved by extrapolation algorithm using the extrapolation algorithm we can improve the convergence order from o h 0 2 to o h 0 3 or even o h 0 4 since the numerical solution of each point is obtained by assignment operation and iteration the computational complexity can be greatly reduced finally four numerical examples are given to illustrate the effectiveness of the method

richardson extrapolation of iterated discrete galerkin solution for two dimensional fredholm integral equations in this paper we study the numerical solution of two dimensional fredholm integral equation by discrete galerkin and iterated discrete galerkin method we are able to derive an asymptotic error expansion of the iterated discrete galerkin solution this expansion covers arbitrarily high powers of the discretization parameters if the solution of the integral equation is smooth the expansion gives rise to richardson type extrapolation schemes which rapidly improve the original rate of the convergence numerical experiments confirm our theoretical results

comments on solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method tari et al a tari m y rahimi s shahmorad f talati solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method j comput appl math 228 2009 70 76 presented some fundamental properties of tdtm for the kernel functions in two dimensional volterra integral equations here we suggest simple proofs of those fundamental properties by using the basic properties of tdtm furthermore we present some fundamental properties of tdtm for the kernel functions of a quotient type in two dimensional volterra integral equations numerical illustrations are demonstrated to show the effectiveness of the tdtm for solving two dimensional volterra integral equations

simulation evaluation of gibbs prior distributions for use in maximum a posteriori spect reconstructions the effects of several of gibbs prior distributions in terms of noise characteristics edge sharpness and overall quantitative accuracy of the final estimates obtained from an iterative maximum a posteriori map procedure applied to data from a realistic chest phantom are demonstrated the effects of the adjustable parameters built into the prior distribution on these properties are examined it is found that these parameter values influence the noise and edge characteristics of the final estimate and can generate reconstructions closer to the actual solution than maximum likelihood ml in addition it is found that the choice of the shape of the prior distribution affects the noise characteristics and edge sharpness in the final estimate

optimal linear filtering under parameter uncertainty this paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state output and input matrices the design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty the results provided generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured assuming the order of the uncertain system is known the optimal robust linear filter is proved to be of the same order as the order of the system in the present case of convex bounded parameter uncertainty the basic numerical design tools are linear matrix inequality lmi solvers instead of the riccati equation solvers used for the design of robust filters available in the literature to date the paper that contains the most important and very recent results on robust filtering is used for comparison purposes in particular it is shown that under the same assumptions our results are generally better as far as the minimization of a guaranteed error variance is considered some numerical examples illustrate the theoretical results

an integral equation describing an asexual population in a changing environment in this paper we establish the existence of a travelling wave solution to an intrinsically nonlinear differential integral equation arising from the mathematical modelling of an asexual reproduction process the techniques used are fixed point theorems and asymptotic analysis the proofs although abstract give a hint on how to obtain the solutions numerically

solving system of volterra fredholm integral equations with bernstein polynomials and hybrid bernstein block pulse functions this work approximates the unknown functions based on the bernstein polynomials and hybrid bernstein block pulse functions in conjunction with the collocation method for the numerical solution of system of fredholm volterra integral equations in both methods the system of integral equations is approximated by the gauss quadrature formula with respect to the legendre weight function the proposed methods reduce the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical methods moreover the convergence analysis of these algorithms will be shown by preparing some theorems numerical experiments are presented to show the superiority and efficiency of proposed methods in comparison with some other well known methods

about some numerical approaches for mixed integral equations abstract in this paper we tackle on mixed volterra fredholm integral equations as in linear as in non linear cases to the aim to obtain numerical solutions of these models the authors propose in the linear case the direct collocation method using a p order quasi interpolating spline class and in the nonlinear case the fixed point method based on polynomial approximation built by schauder tensor bases the advantages of both methods are outlined and their convergence is studied numerical results confirm the theoretical statements

solving partial differential equations by two dimensional differential transform method using two dimensional differential transform to solve partial differential equations pde is proposed in this study first the theory of two dimensional differential transform is introduced second taking two dimensional differential transform of a pde problem a set of difference equations is derived doing some simple mathematical operations on these equations we can get a closed form series solution or an approximate solution quickly finally three pde problems with constant and variable coefficients are solved by the present method the calculated results are compared very well with those obtained by other analytical or approximate methods

two dimensional differential transform for partial differential equations the differential transform is a numerical method for solving differential equations in this paper we present the definition and operation of the two dimensional differential transform a distinctive feature of the differential transform is its ability to solve linear and nonlinear differential equations partial differential equation of parabolic hyperbolic elliptic and nonlinear types can be solved by the differential transform we demonstrate that the differential transform is a feasible tool for obtaining the analytic form solutions of linear and nonlinear partial differential equation

on the numerical solution of the generalized prandtl equation using variation diminishing splines convergence results are proved for cauchy principal value integrals of the schoenberg variation diminishing splines and its first derivative the use of such splines in the numerical solution of the prandtl and generalized prandtl integral equations is proposed a nystrom type method and a modified nystrom method are used and compared computationally

new approach to solve two dimensional fredholm integral equations abstract in this paper we present an efficient iterative method based on quadrature formula to solve two dimensional nonlinear fredholm integral equations we investigate the convergence analysis of the proposed method the error estimation is given in terms of uniform and partial modulus of continuity in addition we show the numerical stability analysis of the method with respect to the choice of the first iteration finally some numerical experiments confirm the theoretical results and illustrate the accuracy of the method

two dimensional triangular functions and their applications to nonlinear 2d volterra fredholm integral equations two dimensional orthogonal triangular functions 2d tfs are presented as a new set of basis functions for expanding 2d functions their properties are determined and an operational matrix for integration obtained furthermore 2d tfs are used to approximate solutions of nonlinear two dimensional integral equations by a direct method since this approach does not need integration all calculations can be easily implemented and several advantages in reducing computational burdens arise finally the efficiency of this method will be shown by comparison with some numerical results

a new algorithm for the solution of nonlinear two dimensional volterra integro differential equations of high order abstract in this manuscript a new numerical approach is developed for approximating the solution of the one dimensional and two dimensional volterra integro differential equations 2d vides of high order new operational matrices of integration based on shifted jacobi polynomials are presented and used in combination with the collocation method to convert the 2d vide into a system of algebraic equations in addition the convergence analysis of the suggested approach is investigated the efficiency of the algorithm is demonstrated by means of several examples and the results are compared with those given using other numerical schemes

evaluation of mixed crank nicolson scheme and tau method for the solution of klein gordon equation abstract numerical method based on the crank nicolson scheme and the tau method is proposed for solving nonlinear klein gordon equation nonlinear klein gordon equation is reduced by crank nicolson scheme to the system of ordinary differential equations then tau method is used to solve this system by using interpolating scaling functions and operational matrix of derivative the order of convergence is proposed and some numerical examples are included to demonstrate the validity and applicability of the technique the method is easy to implement and produces accurate results

efficient nonlocal means for denoising of textural patterns this paper contributes two novel techniques in the context of image restoration by nonlocal filtering first we introduce an efficient implementation of the nonlocal means filter based on arranging the data in a cluster tree the structuring of data allows for a fast and accurate preselection of similar patches in contrast to previous approaches the preselection is based on the same distance measure as used by the filter itself it allows for large speedups especially when the search for similar patches covers the whole image domain i e when the filter is truly nonlocal however also in the windowed version of the filter the cluster tree approach compares favorably to previous techniques in respect of quality versus computational cost second we suggest an iterative version of the filter that is derived from a variational principle and is designed to yield nontrivial steady states it reveals to be particularly useful in order to restore regular textured patterns

biorthogonal systems for solving volterra integral equation systems of the second kind with the aid of biorthogonal systems in adequate banach spaces the problem of approximating the solution of a system of nonlinear volterra integral equations of the second kind is turned into a numerical method that allows it to be solved numerically

nonlocal means based speckle filtering for ultrasound images in image processing restoration is expected to improve the qualitative inspection of the image and the performance of quantitative image analysis techniques in this paper an adaptation of the nonlocal nl means filter is proposed for speckle reduction in ultrasound us images originally developed for additive white gaussian noise we propose to use a bayesian framework to derive a nl means filter adapted to a relevant ultrasound noise model quantitative results on synthetic data show the performances of the proposed method compared to well established and state of the art methods results on real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image