In the present investigation, we study the re ection of plane waves, that is, Longitudinal displacement wave(P-Wave), Thermal wave(T-Wave) and Mass Di, usive wave(MD-Wave) in thermodi, usion elastic-half medium which is subjected to impedence boundary condition in context of one relaxatioon time theory given by Lord and Shulman theory (L-S) and the Coupled theory (C-T) of thermoelasticity. The expressions of amplitude ratios are obtained numerically and their variation with angle of incidence is presented graphically for a particular model to emphasize on the impact of impedence parameter, relaxation time and di, usion. Some special cases are also deduced.

By using the  nite element p-Version in convection-di usion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the  nite element p-Version is augmentation degrees of freedom. Based on the fact that the  nite element and the meshless methods have similar concept, it is obvious that many ideas in the  nite element can be easily used in the meshless methods. Hence, in this study, the concept of the  nite element p-Version is applied in the LPIM meshfree method. The results prove that increasing degrees of freedom limits arti cial numerical oscillations occurred in very large Peclet numbers.

In this paper, a denoising PDE model based on a combination of the isotropic dif-fusion and total variation models is presented. The new weighted model is able to be adaptive in each region in accordance with the image's information. The model performs more di, usion in the at regions of the image, and less di, usion in the edges of the image. The new model has more ability to restore the image in terms of peak signal to noise ratio and visual quality, compared with total variation, isotropic di, usion, and some well-known models. Experimental results show that the model is able to suppress the noise e, ectively while preserving texture features and edge information well.

Error estimates for element schemes for time-dependent for convection-di, usionreaction equations with memory are derived and stated. For the spatially discrete scheme, optimal order error estimates in L2,H1,and W1, p norms for 2 ,p < 1,are obtained. In this paper, we also study the lumped mass modi, cation. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived.

In this paper, we concern ourselves with the study of a class of stationary states for reaction-di, usion systems with densities having disjoint supports. Major contri-bution of this work is computing the numerical solution of problem as the rate of interaction between two di, erent species tend to in, nity. The main di, culty is the nonlinearity nature of problem. To do so, an e, cient iterative method is proposed by hybrid of the radial basis function (RBF) collocation and , nite di, erence (FD) methods to approximate the solution. Numerical results with good accuracies are achieved where the shape parameter is carefully selected. Finally, some numerical examples are given to illustrate the good performance of the method.

In this paper a  nite di erence method for solving 2-dimensional di usion equation is presented. The method employs Crank-Nicolson scheme to improve -nite di erence formulation and its convergence and sta-bility. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the speci c form of obtained matri-ces, rather than solving the problem in each step using conventional iterative methods, a closed-form solution is formulated.

This paper deals with the numerical treatment of singularly perturbed parabolic reaction-di, usion initial boundary value problems. Introducing a , tting parameter into the asymptotic solution and applying average , nite di, erence approximation, a , tted operator , nite di, erence method is developed for solving the problem. To ac-celerate the rate of convergence of the method, Richardson extrapolation technique is applied. The consistency and stability of the proposed method have been established very well to ensure the convergence of the method. Numerical experimentation is carried out on some model problems and both the results are presented in tables and graphs. The numerical results are compared with , ndings of some methods existing in the literature and found to be more accurate. Generally, the formulated method is consistent, stable, and more accurate than some methods existing in the literature for solving singularly perturbed parabolic reaction-di, usion initial boundary value problems.

In the present paper, the spectral meshless radial point interpolation (SMRPI) tech-nique is applied to the solution of pattern formation in nonlinear reaction-di, usion systems. Firstly, we obtain a time discrete scheme by approximating the time deriva-tive via a , nite di, erence formula, then we use the SMRPI approach to approximate the spatial derivatives. This method is based on a combination of meshless meth-ods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as ba-sis functions in the frame of SMRPI. In the current work, the thin plate splines (TPS) are used as the basis functions and in order to eliminate the nonlinearity, a simple predictor-corrector (P-C) scheme is performed. The e, ect of parameters and conditions are studied by considering the well known Brusselator model. Two test problems are solved and numerical simulations are reported which con, rm the e, ciency of the proposed scheme.