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A two-dimensional Haar wavelets method for solving systems of PDEs

Author

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  • Arbabi, Somayeh
  • Nazari, Akbar
  • Darvishi, Mohammad Taghi

Abstract

In this paper, we modify the idea of Haar wavelets method to obtain semi-analytical solutions for the systems of three-dimensional nonlinear partial differential equations. Theoretical considerations are discussed. To demonstrate the efficiency of the method, a test problem is presented. The approximate solutions of the system of three-dimensional nonlinear partial differential equations are compared with the exact solutions as well as existing numerical solutions found in the literature. The numerical solutions which are obtained using the suggested method show that numerical solutions are in a very good coincidence with the exact solutions.

Suggested Citation

  • Arbabi, Somayeh & Nazari, Akbar & Darvishi, Mohammad Taghi, 2017. "A two-dimensional Haar wavelets method for solving systems of PDEs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 33-46.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:33-46
    DOI: 10.1016/j.amc.2016.07.032
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    Cited by:

    1. Abdul Ghafoor & Sirajul Haq & Manzoor Hussain & Poom Kumam & Muhammad Asif Jan, 2019. "Approximate Solutions of Time Fractional Diffusion Wave Models," Mathematics, MDPI, vol. 7(10), pages 1-15, October.
    2. Haq, Sirajul & Ghafoor, Abdul & Hussain, Manzoor, 2019. "Numerical solutions of variable order time fractional (1+1)- and (1+2)-dimensional advection dispersion and diffusion models," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 107-121.

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