A three step superconvergent algorithm for the solution of generalized Burgers’-Huxley and Burgers’-Fisher equations

Document Type : Original Paper


Department of Mathematics, University of Kurdistan, Sanandaj, Iran


In this paper, a new three-step method based on cubic spline will be construct to the numerical solution of a class of partial differential equations well-known as Burgers’-Huxley and Burgers’-Fisher. As we know, the maximum order achieved using cubic spline for interpolating is , but this order is reduced when it is used for the solution of differential equations. Here we will find an  superconvergent approximation for the solution of Burgers’-Huxley and Burgers’-Fisher equations by defining some proper end conditions and constructing a three step deferred-correction algorithm. We will discuss the convergence and error bounds of the method using Green’s function definition in details. In addition, to verify the obtained error bounds, some numerical examples will be presented. Finally, we will try to show the applicability and efficiency of the method by comparing the results with other existing methods.


Main Subjects

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Volume 7, Issue 1
August 2017
Pages 117-137
  • Receive Date: 29 December 2016
  • Revise Date: 23 August 2017
  • Accept Date: 18 July 2017
  • First Publish Date: 23 August 2017