An algorithm based on DQM with modified trigonometric cubic Bsplines for solving coupled viscous Burgers equations

TL;DR

This paper introduces a modified trigonometric cubic B-spline differential quadrature method for solving time-dependent PDEs like the Burgers equation, demonstrating improved accuracy and stability over existing schemes.

Contribution

The paper develops a new differential quadrature method using modified trigonometric cubic B-splines and applies it to Burgers equations, showing enhanced performance.

Findings

The method achieves higher accuracy than existing schemes.

It demonstrates conditional stability through matrix stability analysis.

Numerical tests confirm improved efficiency and precision.

Abstract

This paper deals with a new algorithm called modified trigonometric cubic B-spline differential quadrature method for numerical computation of the time dependent partial differential equations. Specially the numerical computation of the Burgers equation is obtained by using modified trigonometric cubic B spline differential quadrature method with time integration algorithm. The modified trigonometric cubic B-spline differential quadrature method is differential quadrature method with modified trigonometric cubic B-splines as new basis. The initial boundary value system of Burgers equation is first transformed into an initial value system of ordinary differential equations by means of modified trigonometric cubic B-spline differential quadrature method. The resulting system of ordinary differential equations is solved by using an optimal five stage four order strong stability preserving RK method. The accuracy and efficiency of the method is illustrated by five test problems in terms of and error norms and their comparisons with existing results. The modified trigonometric cubic B-spline differential quadrature method produces better results than the results due to almost all the existing schemes. The modified trigonometric cubic B-spline differential quadrature method is shown conditionally stable using the matrix stability analysis method for various grid points.