A Trigonometric Cubic B-spline Finite Element Method for Solving the Nonlinear Coupled Burger Equation

TL;DR

This paper introduces a novel trigonometric cubic B-spline collocation method combined with Crank-Nicolson time integration to efficiently solve the nonlinear coupled Burgers equation, demonstrating high accuracy through multiple test problems.

Contribution

The paper presents a new numerical approach that integrates trigonometric cubic B-splines with collocation and Crank-Nicolson methods for solving coupled nonlinear PDEs.

Findings

High accuracy demonstrated on test problems

Efficient solution of nonlinear algebraic systems

Effective handling of coupled Burgers equations

Abstract

The coupled Burgers equation is solved by way of the trigonometric B-spline collocation method. The unknown of the coupled Burgers equation is integrated in time by aid of the Crank-Nicolson method. Resulting time-integrated coupled Burgers equation is discretized using the trigonometric cubic B-spline collocation method. Fully-integrated couupled Burgers equation which is a system of nonlinear algebraic equation is solved with a variant of Thomas algorithm. The three model test problems are studied to illustrate the accuracy of the suggested method.