NUMERICAL SOLUTIONS OF TIME FRACTIONAL KORTEWEGñDE VRIES EQUATION AND ITS STABILITY ANALYSIS

Abstract

In this study, the fractional derivative and Önite di§erence operators are analyzed. The time fractional KdV equation with initial conditionis considered. Discretized equation is obtained with the help of Önite di§erence operators and used Caputo formula. The inherent truncation errors in themethod are deÖned and analyzed. Stability analysis is explored to demonstratethe accuracy of the method. While doing this analysis, considering conservation law, with the help of using the deÖnition discovered by Lax-Wendro§,von Neumann stability analysis is applied. The numerical solutions of timefractional KdV equation are obtained by using Önite di§erence method. Thecomparison between obtained numerical solutions and exact solution from existing literature is made. This comparison is highlighted with the graphs aswell. Results are presented in tables using the Mathematica software packagewherever it is needed.