Non-central m-point formula in method of lines for solving the Korteweg-de Vries (KdV) equation

Abstract

AbstractThe present study is committed to devising efficient spatial discretization with two non-central difference formulae incorporated in the method of lines (MOL). The method is then implemented numerically on the renowned dispersive evolution equation, the Korteweg-de Vries (KdV) model while infusing Euler and fourth-order Rung-Kutta (RK4) methods, respectively. The resulting schemes are proven to be numerically stable using Fourier’s stability approach, with the MOL matrix admitting negative real eigenvalues. Moreover, this proposal has been assessed on certain initial-boundary value problems of the KdV model by examining so many factors, like the percentage errors, absolute error differences, the error norms, and the invariants $$I_{k},$$ I k , for $$k=1,2,3,$$ k = 1 , 2 , 3 , among others. In this work, we solve KdV by applying a new approach of MOL to improve the results presented in some published articles. Lastly, the assessment revealed that our proposal was found to be better than those of the exponential finite-difference method (Exponential) and the Heat Balance Integral (HBI) methods, respectively, which serve as competing approaches for validation, in terms of both the accuracy and efficiency. The numerical examples are obtained by using MATLAB.