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International Journal of Computer Mathematics Volume 95, 2018 - Issue 6-7: Advances on Computational Fractional Partial Differential Equations
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Original Articles

Fourth-order methods for space fractional reaction–diffusion equations with non-smooth data

Khaled M. FuratiDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
,
M. YousufDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi ArabiaCorrespondence[email protected]
ORCID Iconhttp://orcid.org/0000-0003-3893-4776
ORCID Icon &
A. Q. M. KhaliqDepartment of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN, USA
Pages 1240-1256 | Received 28 Apr 2017, Accepted 29 Sep 2017, Published online: 18 Dec 2017

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Mostafa Abbaszadeh & Mehdi Dehghan. (2021) Fourth-order alternating direction implicit difference scheme to simulate the space-time Riesz tempered fractional diffusion equation. International Journal of Computer Mathematics 98:11, pages 2137-2155.
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J. Alba-Pérez & J. E. Macías-Díaz. (2021) A positive and bounded convergent scheme for general space-fractional diffusion-reaction systems with inertial times. International Journal of Computer Mathematics 98:6, pages 1071-1097.
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Dongdong Hu & Xuenian Cao. (2020) A fourth-order compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equation. International Journal of Computer Mathematics 97:9, pages 1928-1948.
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J. E. Macías-Díaz. (2019) On the solution of a Riesz space-fractional nonlinear wave equation through an efficient and energy-invariant scheme. International Journal of Computer Mathematics 96:2, pages 337-361.
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Articles from other publishers (18)

Muhammad Yousuf & Shahzad Sarwar. (2023) Highly Efficient Numerical Algorithm for Nonlinear Space Variable-Order Fractional Reaction–Diffusion Models. Fractal and Fractional 7:9, pages 688.
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Ibrahim O. Sarumi, Khaled M. Furati, Kassem Mustapha & Abdul Q. M. Khaliq. (2022) Efficient high-order exponential time differencing methods for nonlinear fractional differential models. Numerical Algorithms 92:2, pages 1261-1288.
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J.E. Macías-Díaz. (2022) Design and analysis of a dissipative scheme to solve a generalized multi-dimensional Higgs boson equation in the de Sitter space–time. Journal of Computational and Applied Mathematics 404, pages 113120.
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Naeem Ullah, Muhammad Imran Asjad, Jan Awrejcewicz, Taseer Muhammad & Dumitru Baleanu. (2022) On soliton solutions of fractional-order nonlinear model appears in physical sciences. AIMS Mathematics 7:5, pages 7421-7440.
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Yongho Kim, Gilnam Ryu & Yongho Choi. (2021) Fast and Accurate Numerical Solution of Allen–Cahn Equation. Mathematical Problems in Engineering 2021, pages 1-12.
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Romeo Martínez, Jorge E. Macías-Díaz & Qin Sheng. (2021) An implicit semi-linear discretization of a bi-fractional Klein–Gordon–Zakharov system which conserves the total energy. Applied Numerical Mathematics 169, pages 179-200.
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Shahzad Sarwar, Khaled M. Furati & Muhammad Arshad. (2021) Abundant wave solutions of conformable space-time fractional order Fokas wave model arising in physical sciences. Alexandria Engineering Journal 60:2, pages 2687-2696.
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Ibrahim O. Sarumi, Khaled M. Furati, Abdul Q. M. Khaliq & Kassem Mustapha. (2021) Generalized Exponential Time Differencing Schemes for Stiff Fractional Systems with Nonsmooth Source Term. Journal of Scientific Computing 86:2.
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Romeo Martínez & Jorge E. Macías-Díaz. (2020) An energy-preserving and efficient scheme for a double-fractional conservative Klein–Gordon–Zakharov system. Applied Numerical Mathematics 158, pages 292-313.
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Luis F. Muñoz-Pérez & J.E. Macías-Díaz. (2020) On the solution of a generalized Higgs boson equation in the de Sitter space-time through an efficient and Hamiltonian scheme. Journal of Computational Physics 417, pages 109568.
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J.E. Macías-Díaz. (2020) An easy-to-implement parallel algorithm to simulate complex instabilities in three-dimensional (fractional) hyperbolic systems. Computer Physics Communications 254, pages 107383.
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M. Yousuf, K.M. Furati & A.Q.M. Khaliq. (2020) High-order time-stepping methods for two-dimensional Riesz fractional nonlinear reaction–diffusion equations. Computers & Mathematics with Applications 80:1, pages 204-226.
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Ibrahim O. Sarumi, Khaled M. Furati & Abdul Q. M. Khaliq. (2020) Highly Accurate Global Padé Approximations of Generalized Mittag–Leffler Function and Its Inverse. Journal of Scientific Computing 82:2.
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S.S. Alzahrani, A.Q.M. Khaliq, T.A. Biala & K.M. Furati. (2019) Fourth-order time stepping methods with matrix transfer technique for space-fractional reaction-diffusion equations. Applied Numerical Mathematics 146, pages 123-144.
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J.E. Macías-Díaz. (2019) A parallelized computational model for multidimensional systems of coupled nonlinear fractional hyperbolic equations. Journal of Computational Physics, pages 109043.
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A.S. Hendy & J.E. Macías-Díaz. (2019) A numerically efficient and conservative model for a Riesz space-fractional Klein–Gordon–Zakharov system. Communications in Nonlinear Science and Numerical Simulation 71, pages 22-37.
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Jalil Rashidinia & Elham Mohmedi. (2018) Convergence analysis of tau scheme for the fractional reaction-diffusion equation. The European Physical Journal Plus 133:10.
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Kolade M. Owolabi. (2018) Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator. The European Physical Journal Plus 133:3.
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