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Two Hybrid Methods for Solving Two‐Dimensional Linear Time‐Fractional Partial Differential Equations

Author

Listed:
  • B. A. Jacobs
  • C. Harley

Abstract

A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time‐fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time‐marching to a particular point in time.

Suggested Citation

  • B. A. Jacobs & C. Harley, 2014. "Two Hybrid Methods for Solving Two‐Dimensional Linear Time‐Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:757204
    DOI: 10.1155/2014/757204
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    References listed on IDEAS

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    1. Fukang Yin & Junqiang Song & Fengshun Lu & Hongze Leng, 2012. "A Coupled Method of Laplace Transform and Legendre Wavelets for Lane‐Emden‐Type Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. A. A. Hemeda, 2013. "Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Fukang Yin & Junqiang Song & Yongwen Wu & Lilun Zhang, 2013. "Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, November.
    5. Junqiang Song & Fukang Yin & Xiaoqun Cao & Fengshun Lu, 2013. "Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. Hasan Bulut & Haci Mehmet Baskonus & Yusuf Pandir, 2013. "The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Fukang Yin & Junqiang Song & Xiaoqun Cao & Fengshun Lu, 2013. "Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    8. Fukang Yin & Junqiang Song & Fengshun Lu & Hongze Leng, 2012. "A Coupled Method of Laplace Transform and Legendre Wavelets for Lane-Emden-Type Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-16, November.
    9. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    10. Limei Yan, 2013. "Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, December.
    11. Fukang Yin & Junqiang Song & Yongwen Wu & Lilun Zhang, 2013. "Numerical Solution of the Fractional Partial Differential Equations by the Two‐Dimensional Fractional‐Order Legendre Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    12. Hasan Bulut & Haci Mehmet Baskonus & Yusuf Pandir, 2013. "The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    13. Fukang Yin & Junqiang Song & Xiaoqun Cao & Fengshun Lu, 2013. "Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, February.
    14. A. A. Hemeda, 2013. "Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, December.
    15. Limei Yan, 2013. "Numerical Solutions of Fractional Fokker‐Planck Equations Using Iterative Laplace Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    16. Junqiang Song & Fukang Yin & Xiaoqun Cao & Fengshun Lu, 2013. "Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, February.
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