Quintic B-spline collocation method for numerical solution of the Kuramoto–Sivashinsky equation

Numerical solution of the coupled viscous Burgers’ equation

“…The use of various degree of B-spline functions in getting the numerical solution of some partial differential equations are shown to provide easy and simple algorithms, as an example, cubic B-spline collocation method is used in [12,13]. Quintic B-spline collocation method is used to find numerical solution of some nonlinear equations in [14,15].…”

Collocation method using quintic B-spline and sinc functions for solving a model of squeezing flow between two infinite plates

“…As said in [41], the collocation method with B-spline approximations represents an economical alternative since it only requires the evaluation of the unknown parameters at the grid points. The quintic B-splines have been employed to solve Kuramoto-Sivashinsky equation [20], fourth order partial integro-differential equations [41], fourth-order parabolic partial differential equations [4] and second order mixed boundary value problem [17]. Also, there have been numerous applications of B-spline functions.…”

“…Consider the B-splines basis in S 5 (I). The quintic B-splines B i (z), (i = −2, ..., N + 2) can be defined by [17,20] …”

B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equations

“…In Section 6, we present the way to obtain the initial state which is required to start our scheme I. In Section 7, we present Method-II, based on quintic B-spline collocation method with redefined basis function [1,16,22] for non-homogeneous equation. In Section 8, implementation process of method II is described.…”