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Volume 6 Issue 1
Jan.  2019

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2019  >  6(1): 299-306
Hossein Aminikhah, Mahdieh Tahmasebi and Mahmoud Mohammadi Roozbahani, "The Multi-scale Method for Solving Nonlinear Time Space Fractional Partial Differential Equations," IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 299-306, Jan. 2019. doi: 10.1109/JAS.2016.7510058
Citation: Hossein Aminikhah, Mahdieh Tahmasebi and Mahmoud Mohammadi Roozbahani, "The Multi-scale Method for Solving Nonlinear Time Space Fractional Partial Differential Equations," IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 299-306, Jan. 2019. doi: 10.1109/JAS.2016.7510058
shu

The Multi-scale Method for Solving Nonlinear Time Space Fractional Partial Differential Equations

doi: 10.1109/JAS.2016.7510058
  • 1.

    Department of Applied Mathematics, University of Guilan, Rasht 41938-19141, Iran

  • 2.

    Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-137, Iran

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    Abstract
  • In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.

     

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