A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative

Abstract

In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have been approximated by first and second derivatives of the cubic B-spline quasi-interpolation. The discrete scheme obtained in this way constitutes a system of algebraic equations associated with a bi-pentadiagonal matrix. We show that the proposed scheme is unconditionally stable. Numerical examples are provided to verify the efficiency of the method.

On spline quasi-interpolation through dimensions

“…Moreover, if we narrow our Scopus Research in the "Article Title/Abstract/Keywords" field, adding also the word spline (accessed on June 24, 2022) we obtain 367 papers and if we consider the papers published from 2017, we can also mention the following works, subdividing them into different topics. In particular, [62,79] deal with the construction and study of new quasi-interpolating operators, in [12,48,59] generalized spline quasi-interpolants are proposed, in [1,20,[49][50][51]53] new integration formulas based on spline quasi-interpolants are constructed, in [15,54,61,63,64,80,81,84] and [4,11] quasi-interpolants are used for the numerical approximation of the solution of differential and integral equations, respectively. Furthermore, in [7,16,17,23,52,65,66] quasi-interpolants are used in different areas of science and engineering: imaging, Computer Aided Geometric Design, industry, etc.…”