Numerical solutions of nonhomogeneous Rosenau type equations by quintic B‐spline collocation method

Abstract

In this study, a numerical scheme based on a collocation finite element method using quintic B‐spline functions for getting approximate solutions of nonhomogeneous Rosenau type equations prescribed by initial and boundary conditions is proposed. The numerical scheme is tested on four model problems with known exact solutions. To show how accurate results the proposed scheme produces, the error norms defined by L2 and L∞ are calculated. Additionally, the stability analysis of the scheme is done by means of the von Neuman method.

Numerical Simulation of Generalized Oskolkov Equation via the Septic B-Spline Collocation Method

“…Nonlinear evolution equations (NLEEs) are special classes of the category of partial differential equations (PDEs), which have been studied intensively in past several decades [1]. Various methods [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] have been devised to find the exact and approximate solutions of PDEs in order to provide more information for understanding physical phenomena arising in numerous scientific and engineering fields such as mathematics, physics, mechanics, biology, ecology, optical fiber, chemical reaction and so on [18].…”