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The bivariate Müntz wavelets composite collocation method for solving space-time-fractional partial differential equations

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Abstract

Herein, we consider an effective numerical scheme for numerical evaluation of three classes of space-time-fractional partial differential equations (FPDEs). We are going to solve these problems via composite collocation method. The procedure is based upon the bivariate Müntz–Legendre wavelets (MLWs). The bivariate Müntz–Legendre wavelets are constructed for first time. The bivariate MLWs operational matrix of fractional-order integral is constructed. The proposed scheme transforms FPDEs to the solution of a system of algebraic equations which these systems will be solved using the Newton’s iterative scheme. Also, the error analysis of the suggested procedure is determined. To test the applicability and validity of our technique, we have solved three classes of FPDEs.

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Acknowledgements

The second author is supported by the Alzahra university within project 97/1/216. Also, we express our sincere thanks to the anonymous referees for valuable suggestions that improved the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

    Parisa Rahimkhani & Yadollah Ordokhani

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  1. Parisa Rahimkhani
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  2. Yadollah Ordokhani
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Correspondence to Yadollah Ordokhani.

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Communicated by Vasily E. Tarasov.

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Rahimkhani, P., Ordokhani, Y. The bivariate Müntz wavelets composite collocation method for solving space-time-fractional partial differential equations. Comp. Appl. Math. 39, 115 (2020). https://doi.org/10.1007/s40314-020-01141-7

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