An efficient scheme for solving nonlinear generalized kuramoto-sivashinksy processes

Abstract

In this work, we investigate the numerical solution of generalized Kuramoto-Sivashinksy (GKS) problems based on the collocation of the quantic B-spline (QBS) and high-order strong stability-preserving Runge–Kutta (SSPRK54) scheme. When considering nonlinear parts that lose real features, we address the issue without resorting to any transformations or linearization. The efficiency and accuracy of our proposed technique are evaluated using a variety of illustrative examples. The numerical results show that our approach captured the natural behaviour of the problems well and consumed less storage space.