Modelling solitary wave via numerical solution of Korteweg de Vries and KdV-Burger equation using differential quadrature

Abstract

The prime objective of the coastal engineering community is to protect near-shore areas. Because they lessen shock from single waves near coastal locations, artificial structures may protect the near-shore areas. A single wave propagates without changing shape or size. The mathematical description of solitary wave explains that the global peak of solitary wave decays gradually far away from the peak. The solitary wave can be obtained by solving the 'Korteweg de Vries (KdV) ' equation analytically or numerically and also develops a numerical solver of the KdV equation to understand the behaviour of travelling waves. The research is also extended to develop the numerical solution of the KdV-Burger equation to understand the travelling characteristics of heat waves. Traditional finite difference methods can be applied to have the corresponding numerical solutions. However, in this research, the challenge is to develop numerical solutions of KdV and KdV-Burger equations using an innovative numerical method such as differential quadrature. The basic idea of differential quadrature is to approximate partial derivatives of any order as a matrix. L2 norm and L∞ are computed for stability analysis of the outcome of the differential quadrature method.