Numerical solution of advection–diffusion type equation by modified error correction scheme

A numerical solution of Burgers' equation by modified Adomian method

In this paper, the modified Adomian s decomposition method for calculating a numerical solution of the one-dimensional quasi-linear, the Burgers equation, is presented. Time discretization has been used in decomposition, without using any transformation in the Burgers equation such as Hopf–Cole transformation. The numerical results obtained by this way for various values of viscosity have been ...

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

A numerical solution of Burger’s equation based on modified extended BDF scheme

Department of Mathematics, Faculty of science, Razi university, Kermanshah 67149, Iran. Abstract In this paper, we present a new method for solving of the Burger’s equation by combination of method of lines (MOL) and matrix free modified extended backward differential formula (MF-MEBDF). The method of lines semi discretization approach is used to transform the model partial differential equatio...

Unconditionally Stable Difference Scheme for the Numerical Solution of Nonlinear Rosenau-KdV Equation

In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...