An Exponential Cubic B-spline Finite Element Method for Solving the Nonlinear Coupled Burger Equation

TL;DR

This paper introduces an exponential cubic B-spline finite element method combined with Crank-Nicolson for numerically solving the nonlinear coupled Burgers' equation, demonstrating high accuracy across multiple test problems.

Contribution

The paper presents a novel exponential cubic B-spline collocation scheme integrated with Crank-Nicolson for improved numerical solutions of the nonlinear coupled Burgers' equation.

Findings

Proposed method yields highly accurate results.

Compared favorably with existing numerical schemes.

Effective across different test problems.

Abstract

The exponential cubic B-spline functions together with Crank Nicolson are used to solve numerically the nonlinear coupled Burgers' equation using collocation method. This method has been tested by three different problems. The proposed scheme is compared with some existing methods. We have noticed that proposed scheme produced a highly accurate results.