A new optimization operational matrix algorithm for solving nonlinear variable-order time fractional convection-diffusion equation

Document Type : Original Paper

Authors

1 Department of َApplied Mathematics, Shahrekord University, Shahrekord , Iran

2 Department of Mathematics, Yasouj University, Yasouj, Iran.

Abstract

In this paper, a new and effective optimization algorithm is proposed for solving the nonlinear time fractional convection-diffusion equation with the concept of variable-order fractional derivative in the Caputo sense. For finding the solution, we first introduce the generalized polynomials (GPs) and construct the variable-order operational matrices. In the proposed optimization technique, the solution of the problem under consideration is expanded in terms of GPs with unknown free coefficients and control parameters. The main advantage of the presented method is to convert the variable-order fractional partial differential equation to a system of nonlinear algebraic equations. Also, we obtain the free coefficients and control parameters optimally by minimizing the error of the approximate solution. Finally, the numerical examples confirm the high accuracy and efficiency of the proposed method in solving the problem under study.

Keywords

Main Subjects

References

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Journal of Advanced Mathematical Modeling
Volume 9, Issue 1
March 2019
Pages 98-119

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History

  • Receive Date: 17 December 2017
  • Revise Date: 10 October 2018
  • Accept Date: 30 October 2018

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