A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation

Document Type : Research Paper


1 Engineering Sciences, Faculty of Architecture and Engineering, Izmir Katip Celebi University, Izmir, Turkey.

2 Management Information Systems, Faculty of Economics and Administrative Sciences, Dogus University, Istanbul, Turkey.

3 Department of Civil Engineering, Pamukkale University, Denizli, Turkey.

4 Department of Mathematics, Izmir Institute of Technology, Izmir, Turkey.


In this article, the coupled Burger’s equation which is one of the known systems of the nonlinear parabolic partial differential equations is studied. The method presented here is based on a combination of the quintic B-spline and a high order time integration scheme known as adaptive Runge-Kutta method. First of all, the application of the new algorithm on the coupled Burger’s equation is presented. Then, the convergence of the algorithm is studied in a theorem. Finally, to test the efficiency of the new method, coupled Burger’s equations in literature are studied. We observed that the presented method has better accuracy and efficiency compared to the other methods in the literature.


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Volume 11, Issue 1
January 2023
Pages 130-142
  • Receive Date: 01 April 2022
  • Revise Date: 14 June 2022
  • Accept Date: 15 June 2022
  • First Publish Date: 15 June 2022