Computational method to solve Burgers' equation with periodic boundary conditions

  • Amit Tripathi Department of Applied Science \& Humanities, Rajkiya Engineering College Banda
  • Anand Kumar Tiwari Department of Applied Science, Indian Institute of Information Technology, Allahabad \\ Uttar Pradesh-211 015, India
  • S. Dhawan Department of Mathematics, CCSHAU COAB, Haryana, India.
  • Ramu Dubey Department of Mathematics, J. C. Bose University of Science \& Technology, YMCA, Faridabad\\ Haryana-121006, India

Abstract

This research study presents a computational scheme to analyze Burgers' equation with periodic borders which models diffusive shock wave in viscous medium. To discretize the equation in space, the collocation method using Cubic B-splines is employed. Proposed approach converts the Burgers' equation into system of ODEs, which is further solved by Runge-kutta method. The computational complexity of scheme is also determined in terms of number on operation and found to be $O(M)$, where the overall number of nodes in space is denoted by $M$. Proposed strategy is applied to several examples and solutions are observed quite satisfactory and proficient with the existing findings from past research investigations. The scheme's stability is also examined and stability conditions have been deduced on time step.

Published
2024-05-24