Numerical Solution of Nonlinear Partial Differential Equation Using Runge-Kutta 6th Order Method
8 Pages Posted: 25 Mar 2019 Last revised: 3 Apr 2019
Date Written: March 1, 2019
The nonlinear waves play an important role in applied mathematics, these waves are modeled by Nonlinear Partial Differential Equations (NPDEs). Many different numerical methods are available to solve this type of equations, The main objective of this paper is to employ Runge-Kutta method of 6th order with seven stages (RK6) to find the numerical solution of NPDE, the method requires more calculations, but provides butter accuracy, the accuracy of the method is tested using exact and the semi-numerical-analytic Differential Transform Method (DTM), finally some illustration examples are presented to explain the method.
Keywords: Nonlinear Partial Differential Equations, Laplace Decomposition Method, Differential Transform Method, Runge-Kutta Method of 6th Order
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