Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers' Equation


Oruc O., Bulut F., Esen A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.48, no.1, pp.1-16, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.15672/hjms.2018.642
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1-16
  • Keywords: Chebyshev wavelet method, Chebyshev collocation, coupled Burgers' equation, nonlinear phenomena, numerical solution, PARTIAL-DIFFERENTIAL-EQUATIONS, SOLVING BURGERS, INTEGRODIFFERENTIAL EQUATIONS, COLLOCATION METHOD, TRANSFORMATION, SIMULATION, 2D

Abstract

This paper deals with the numerical solutions of one dimensional time dependent coupled Burgers' equation with suitable initial and boundary conditions by using Chebyshev wavelets in collaboration with a collocation method. The proposed method converts coupled Burgers' equations into system of algebraic equations by aid of the Chebyshev wavelets and their integrals which can be solved easily with a solver. Benchmarking of the proposed method with exact solution and other known methods already exist in the literature is made by three test problems. The feasibility of the proposed method is demonstrated by test problems and indicates that the proposed method gives accurate results in short cpu times. Computer simulations show that the proposed method is computationally cheap, fast and quite good even in the case of less number of collocation points.