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Numerical Solution of Time‐Fractional Diffusion‐Wave Equations via Chebyshev Wavelets Collocation Method

Author

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  • Fengying Zhou
  • Xiaoyong Xu

Abstract

The second‐kind Chebyshev wavelets collocation method is applied for solving a class of time‐fractional diffusion‐wave equation. Fractional integral formula of a single Chebyshev wavelet in the Riemann‐Liouville sense is derived by means of shifted Chebyshev polynomials of the second kind. Moreover, convergence and accuracy estimation of the second‐kind Chebyshev wavelets expansion of two dimensions are given. During the process of establishing the expression of the solution, all the initial and boundary conditions are taken into account automatically, which is very convenient for solving the problem under consideration. Based on the collocation technique, the second‐kind Chebyshev wavelets are used to reduce the problem to the solution of a system of linear algebraic equations. Several examples are provided to confirm the reliability and effectiveness of the proposed method.

Suggested Citation

  • Fengying Zhou & Xiaoyong Xu, 2017. "Numerical Solution of Time‐Fractional Diffusion‐Wave Equations via Chebyshev Wavelets Collocation Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:2610804
    DOI: 10.1155/2017/2610804
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    References listed on IDEAS

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    1. Zhi Mao & Aiguo Xiao & Zuguo Yu & Long Shi, 2014. "Finite Difference and Sinc-Collocation Approximations to a Class of Fractional Diffusion-Wave Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, July.
    2. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
    3. Zhi Mao & Aiguo Xiao & Zuguo Yu & Long Shi, 2014. "Finite Difference and Sinc‐Collocation Approximations to a Class of Fractional Diffusion‐Wave Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. Sweilam, N.H. & Nagy, A.M. & El-Sayed, Adel A., 2015. "Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 141-147.
    5. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second‐Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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