Soliton solution of coupled Korteweg-de Vries equation by quintic UAH tension B-spline differential quadrature method

Abstract

The concern of this paper is to acquire the numerical solution of Coupled Korteweg-de Vries (CKdV) equation describing the behaviour of shallow water surfaces in terms of solitons. A new regime quintic Uniform Algebraic Hyperbolic (QUAH) tension B-spline with a very well-known method called Differential Quadrature Method (DQM) is used. Over the past few years, the idea of consuming DQM to solve partial differential equations numerically has acknowledged much consideration all over the science community. Initially, the QUAH tension B-spline is used as a basis function in DQM to solve the weighting coefficients. After calculating weighting coefficients, the basis function converts the Initial boundary value problem into an ordinary differential equation, which is further solved by using a strong preserving Runge-Kutta 43 regime. Then, to check the accuracy and amendment of the used method, different test problems are solved numerically as well as error norms L2 and L∞ are calculated. Calculated results are shown graphically and in tabular form for quick and easy access. An obtained result gives the insight that the proposed technique is effective and efficient for elucidating the variety of complex partial differential equations.