10.1007/s40096-017-0214-4

Two-dimensional Bernoulli wavelets with satisfier function in the Ritz–Galerkin method for the time fractional diffusion-wave equation with damping

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  • Z. Barikbin*1,
  1. Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, IR
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Published in Issue 2017-02-28

How to Cite

Barikbin, Z. (2017). Two-dimensional Bernoulli wavelets with satisfier function in the Ritz–Galerkin method for the time fractional diffusion-wave equation with damping. Mathematical Sciences, 11(3 (September 2017). https://doi.org/10.1007/s40096-017-0214-4
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Abstract

Abstract In this paper, the two-dimensional Bernoulli wavelets (BWs) with Ritz–Galerkin method are applied for the numerical solution of the time fractional diffusion-wave equation. In this way, a satisfier function which satisfies all the initial and boundary conditions is derived. The two-dimensional BWs and Ritz–Galerkin method with satisfier function are used to transform the problem under consideration into a linear system of algebraic equations. The proposed scheme is applied for numerical solution of some examples. It has high accuracy in computation that leads to obtaining the exact solutions in some cases.

Keywords

  • Two-dimensional Bernoulli wavelets basis,
  • Fractional diffusion-wave equation,
  • Ritz–Galerkin method,
  • Satisfier function,
  • Caputo derivative
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