Computational Sinc-scheme for extracting analytical solution for the model Kuramoto-Sivashinsky equation

Abstract

The present article is designed to supply two different numerical<br />solutions for solving Kuramoto-Sivashinsky equation. We have made<br />an attempt to develop a numerical solution via the use of<br />Sinc-Galerkin method for Kuramoto-Sivashinsky equation, Sinc<br />approximations to both derivatives and indefinite integrals reduce<br />the solution to an explicit system of algebraic equations. The fixed<br />point theory is used to prove the convergence of the proposed<br />methods. For comparison purposes, a combination of a Crank-Nicolson<br />formula in the time direction, with the Sinc-collocation in the<br />space direction is presented, where the derivatives in the space<br />variable are replaced by the necessary matrices to produce a system<br />of algebraic equations. In addition, we present numerical examples<br />and comparisons to support the validity of these proposed<br />methods.

An analytic study of the fractional order model of HIV-1 virus and CD4+ T-cells using adomian method

“…In this paper, we will study a system of FODE which is a valid model for studying the development and growth of HIV, as we begin to define fractional derivatives and fractional integration. [20,21]. Previous studies have shown that there are many definitions of fractional derivatives, and here only we mention the method that we will use which is Caputo's definition, which is suitable for solving differential equations with initial values.…”