Numerical simulations of Kuramoto–Sivashinsky equation in reaction-diffusion via Galerkin method

A conservative algorithm based on a hybrid block method and tension B‐spline differential quadrature method for Rosenau–KdV–RLW equation

“…Recently, the coupled Burgers equation has been solved using DQM based on UAT-tension B-splines [24]. Also, hyperbolic-trigonometric tension B-splines have been used with a Galerkin approach [25,26]. Since UAT tension B-splines attain more desirable properties, we have considered UAT tension B-splines of order 4 as test functions to obtain the weighting coefficients.…”

An efficient scheme for solving nonlinear generalized kuramoto-sivashinksy processes

“…In the previous years, researchers have extensively studied the KS equation using a diverse array of numerical techniques. Ersoy [41] solved KS equation via Galerkin method, Denis S G. [42] used numerical simulations to study how introducing advection affects localized patterns in a system governed by a modified KS equation with frozen disorder, Shah et al [43] presented A semi-analytical method to solve family of KSE, Bhatt and Chowdhury [44] developed a numerical scheme combining a fourth-order Runge-Kutta-based implicitexplicit scheme in time and a compact higher-order finite difference scheme in space, Jena and Gebremedhin [45] applied a nonic B-spline collocation approach to solve the KS equation and they used the Taylor series technique to linearize the nonlinear term of the KS equation during the solution process, Mkhize et al [46] introduced heptic Hermite basis functions, employed them in the orthogonal collocation on finite elements (OCFE) method, and used this approach to solve the GKSE.…”