Numerical Solution of Korteweg-De Vries Equation by Quintic B-Spline Differential Quadrature Method

Abstract

In this manuscript, we have used quintic B-spline functions to get the numerical solutions of the Korteweg-De
Vries (KdV) equation, which is a nonlinear equation. The functions and their derivatives have been approximated
using the quintic B-spline function. By using the Thomas algorithm, we obtained the weighting coefficients of
the differential quadrature method, and the SSP-RK43 scheme has been used to solve differential equations.
The test problem has been solved numerically to demonstrate the effectiveness and accuracy of the method.
Numerical solutions have been presented in tables and illustrated graphically.