The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains
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Abbaszadeh, M., Dehghan, M.: An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate. Numer. Algorithms 75(1), 173–211 (2017)
Aboelenen, T., Bakr, S.A., El-Hawary, H.M.: Fractional Laguerre spectral methods and their applications to fractional differential equations on unbounded domain. Int. J. Comput. Math. 94(3), 570–596 (2017)
Andrews, G.E., Askey, R., Roy, R.: Special functions, volume 71 of encyclopedia of mathematics and its applications (1999)
Arara, A., Benchohra, M., Hamidi, N., Nieto, J.: Fractional order differential equations on an unbounded domain. Nonlinear Anal. Theory Methods Appl. 72(2), 580–586 (2010)
Bateman, H.: Tables of integral transforms. McGraw-Hill, New York (1954)
Bhrawy, A.: A Jacobi spectral collocation method for solving multi-dimensional nonlinear fractional sub-diffusion equations. Numer. Algorithms 73(1), 91–113 (2016)
Bhrawy, A., Abdelkawy, M., Alzahrani, A., Baleanu, D., Alzahrani, E.: A Chebyshev-Laguerre-Gauss-Radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain (2015)
Chandru, M., Das, P., Ramos, H.: Numerical treatment of two-parameter singularly perturbed parabolic convection diffusion problems with non-smooth data. Math. Methods Appl. Sci. 41(14), 5359–5387 (2018)
Chandru, M., Prabha, T., Das, P., Shanthi, V.: A numerical method for solving boundary and interior layers dominated parabolic problems with discontinuous convection coefficient and source terms. Differential Equations and Dynamical Systems. https://doi.org/10.1007/s12591-017-0385-3 (2017)
Chen, H., Lü, S., Chen, W.: Spectral methods for the time fractional diffusion–wave equation in a semi-infinite channel. Comput. Math. Appl. 71(9), 1818–1830 (2016)
Das, P.: Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems. J. Comput. Appl. Math. 290, 16–25 (2015)
Das, P.: An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh. Numerical Algorithms. https://doi.org/10.1007/s11075-018-0557-4 (2018)
Das, P.: A higher order difference method for singularly perturbed parabolic partial differential equations. J. Differ. Equ. Appl. 24(3), 452–477 (2018)
Das, P., Mehrmann, V.: Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters. BIT Numer. Math. 56(1), 51–76 (2016)
Das, P., Natesan, S.: Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction–diffusion boundary-value problems. Appl. Math. Comput. 249, 265–277 (2014)
Das, P., Vigo-Aguiar, J.: Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter. Journal of Computational and Applied Mathematics (2017)
Dehghan, M., Abbaszadeh, M.: Spectral element technique for nonlinear fractional evolution equation, stability and convergence analysis. Appl. Numer. Math. 119, 51–66 (2017)
Dehghan, M., Abbaszadeh, M., Mohebbi, A.: Analysis of a meshless method for the time fractional diffusion-wave equation. Numer. Algorithms 73(2), 445–476 (2016)
Dehghan, M., Abbaszadeh, M., Mohebbi, A.: Legendre spectral element method for solving time fractional modified anomalous sub-diffusion equation. Appl. Math. Model. 40(5-6), 3635–3654 (2016)
Dehghan, M., Manafian, J., Saadatmandi, A.: Solving nonlinear fractional partial differential equations using the homotopy analysis method. Numer. Methods Partial Differ. Equ.: Int. J. 26(2), 448–479 (2010)
Gao, G., Alikhanov, A.A., Sun, Z.: The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations. J. Sci. Comput. 73(1), 93–121 (2017)
Gao, G., Sun, Z., Zhang, Y.: A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions. J. Comput. Phys. 231(7), 2865–2879 (2012)
Gómez-Aguilar, J.: Space–time fractional diffusion equation using a derivative with nonsingular and regular kernel. Physica A: Stat. Mech. Appl. 465, 562–572 (2017)
Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series, and products. Academic Press, New York (2014)
Guo, B., Wang, L., Wang, Z.: Generalized Laguerre interpolation and pseudospectral method for unbounded domains. SIAM J. Numer. Anal. 43(6), 2567–2589 (2006)
Huang, C., Zhang, Z., Song, Q.: Spectral methods for substantial fractional differential equations. J. Sci. Comput. 74(3), 1554–1574 (2018)
Huang, J., Yang, D.: A unified difference-spectral method for time–space fractional diffusion equations. Int. J. Comput. Math. 94(6), 1172–1184 (2017)
Jiang, S., Zhang, J., Zhang, Q., Zhang, Z.: Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations. Commun. Comput. Phys. 21(3), 650–678 (2017)
Jiang, W., Li, H.: A space–time spectral collocation method for the two-dimensional variable-order fractional percolation equations. Comput. Math. Appl. 75(10), 3508–3520 (2018)
Khosravian-Arab, H., Dehghan, M., Eslahchi, M.: Fractional Sturm-Liouville boundary value problems in unbounded domains: theory and applications. J. Comput. Phys. 299, 526–560 (2015)
Khosravian-Arab, H., Dehghan, M., Eslahchi, M.: Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications. J. Comput. Phys. 338, 527–566 (2017)
Lenka, B.K., Banerjee, S.: Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 56, 365–379 (2018)
Li, H., Jiang, W.: A space-time spectral collocation method for the 2-dimensional nonlinear Riesz space fractional diffusion equations. Mathematical Methods in the Applied Sciences
Li, X., Xu, C.: A space-time spectral method for the time fractional diffusion equation. SIAM J. Numer. Anal. 47(3), 2108–2131 (2009)
Li, X., Xu, C.: Existence and uniqueness of the weak solution of the space-time fractional diffusion equation and a spectral method approximation. Commun. Comput. Phys. 8(5), 1016 (2010)
Mao, Z., Shen, J.: Hermite spectral methods for fractional PDEs in unbounded domains. SIAM J. Sci. Comput. 39(5), A1928–A1950 (2017)
Olver, F.W.: NIST Handbook of mathematical functions hardback and CD-ROM. Cambridge University Press, Cambridge (2010)
Parand, K., Shahini, M., Dehghan, M.: Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane–Emden type. J. Comput. Phys. 228(23), 8830–8840 (2009)
Podlubny, I.: Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, vol. 198. Elsevier, New York (1998)
Povstenko, Y.: Fundamental solutions to time-fractional heat conduction equations in two joint half-lines. Open Phys. 11(10), 1284–1294 (2013)
Ren, J., Mao, S., Zhang, J.: Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation. Numer. Methods Partial Differ. Equ. 34(2), 705–730 (2018)
Ren, L., Wang, Y.: A fourth-order extrapolated compact difference method for time-fractional convection-reaction-diffusion equations with spatially variable coefficients. Appl. Math. Comput. 312, 1–22 (2017)
Salehi, R.: A meshless point collocation method for 2-D multi-term time fractional diffusion-wave equation. Numer. Algorithms 74(4), 1145–1168 (2017)
Shan, Y., Liu, W., Wu, B.: Space–time Legendre–Gauss–Lobatto collocation method for two-dimensional generalized Sine-Gordon equation. Appl. Numer. Math. 122, 92–107 (2017)
Shen, J., Tang, T., Wang, L.: Spectral methods: algorithms, analysis and applications, vol. 41. Springer Science & Business Media, Berlin (2011)
Tang, T., Yuan, H., Zhou, T.: Hermite spectral collocation methods for fractional PDEs in unbounded domains. arXiv: 1801.09073.2018 (2018)
Wang, T., Jiao, Y.: A fully discrete pseudospectral method for Fisher’s equation on the whole line. Appl. Numer. Math. 120, 243–256 (2017)
Wei, L.: Analysis of a new finite difference/local discontinuous Galerkin method for the fractional Cattaneo equation. Numer. Algorithms 77(3), 675–690 (2018)
Wei, S., Chen, W., Zhang, J.: Time-fractional derivative model for chloride ions sub-diffusion in reinforced concrete. Eur. J. Environ. Civ. Eng. 21(3), 319–331 (2017)
Yu, H., Wu, B., Zhang, D.: A generalized laguerre spectral Petrov–Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain. Appl. Math. Comput. 331, 96–111 (2018)
Zeng, F., Li, C.: A new Crank–Nicolson finite element method for the time-fractional subdiffusion equation. Appl. Numer. Math. 121, 82–95 (2017)
Zhang, C., Liu, W., Wang, L.: A new collocation scheme using non-polynomial basis functions. J. Sci. Comput. 70(2), 793–818 (2017)
Zhang, Q., Zhang, J., Jiang, S., Zhang, Z.: Numerical solution to a linearized time fractional KDV equation on unbounded domains. Math. Comput. 87 (310), 693–719 (2018)
Zhang, S.: Monotone method for initial value problem for fractional diffusion equation. Sci. China Ser. A: Math. 49(9), 1223–1230 (2006)
Zhao, X., Ge, W.: Unbounded solutions for a fractional boundary value problems on the infinite interval. Acta Appl. Math. 109(2), 495–505 (2010)
Zhao, Z.: Bäcklund transformations, rational solutions and soliton-cnoidal wave solutions of the modified Kadomtsev–Petviashvili equation. Appl. Math. Lett. 89, 103–110 (2019)