Maohua Ran1,2, Chengjian Zhang3
[1] W. Deng, B. Li, W. Tian, P. Zhang, Boundary problems for the fractional and tempered fractional operators, Multiscale Model. Simul., 16:1(2018), 125-149.[2] C. Çelik, M. Duman, Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative, J. Comput. Phys., 231:4(2012), 1743-1750.[3] A. Haghighi, H. Ghejlo, N. Asghari, Explicit and implicit methods for fractional diffusion equations with the Riesz fractional derivative, Indian J. Sci. Technol., 6:7(2013), 4881-4885.[4] H. Ding, C. Li, Y. Chen, High-order algorithms for Riesz derivative and their applications (I), Abstr. Appl. Anal., (2014) Article ID 653797.[5] B. Carreras, V. Lynch, G. Zaslavsky, Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model, Phys. Plasmas, 8:12(2001), 5096-5103.[6] R. Magin, Fractional calculus in bioengineering, Begell House Publishers, 2006.[7] M. Meerschaert, C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math., 172:1(2004), 65-77.[8] M. Ortigueira, Riesz potential operators and inverses via fractional centred derivatives, Int. J. Math. Math. Sci., 2006(2006), 48391.[9] M. Ran, Y. He, Linearized Crank-Nicolson method for solving the nonlinear fractional diffusion equation with multi-delay, Int. J. Comput. Math., doi:10.1080/00207160.2017.1398326, (2017).[10] C. Lubich, Discretized fractional calculus, SIAM J. Numer. Anal., 17:3(1986), 704-719.[11] M. Chen, W. Deng, Fourth order accurate scheme for the space fractional diffusion equations, SIAM J. Numer. Anal., 52:3(2014), 1418-1438.[12] F. Lin, S. Yang, X. Jin, Preconditioned iterative methods for fractional diffusion equation, J. Comput. Phys., 256(2014), 109-117.[13] X. Gu, T. Huang, X. Zhao, H. Li, L. Li, Strang-type preconditioners for solving fractional diffusion equations by boundary value methods, J. Comput. Appl. Math., 277(2015), 73-86.[14] S. Lei, Y. Huang, Fast algorithms for high-order numerical methods for space-fractional diffusion equations, Int. J. Comput. Math., 94:5(2017), 1062-1078.[15] X. Zhao, Z. Sun, Z. Hao, A fourth-order compact ADI scheme for two-dimensional nonlinear space fractional schrödinger equation, SIAM J. Sci. Comput., 36:6(2014), 2865-2886.[16] Z. Hao, Z. Sun, W. Cao, A fourth-order approximation of fractional derivatives with its applications, J. Comput. Phys., 281(2015), 787-805.[17] L. Brugnano and D. Trigiante, Solving Differential Equations by Multistep Initial and Boundary Value Methods, Gordan and Breach, 1998.[18] M. Ran, C. Zhang, New compact difference scheme for solving the fourth-order time fractional sub-diffusion equation of the distributed order, Appl. Numer. Math., 129(2018), 58-70.[19] R. Chan, M. Ng, Conjugate gradient methods for Toeplitz systems, SIAM Rev., 38:3(1996), 427-482.[20] D. Bertaccini, A circulant preconditioner for the systems of LMF-based ODE codes, SIAM J. Sci. Comput., 22:3(2000), 767-786.[21] C. Zhang, H. Chen, Block boundary value methods for delay differential equations, Appl. Numer. Math., 60:9(2010), 915-923.[22] H. Chen, C. Zhang, Boundary value methods for Volterra integral and integro-differential equations, Appl. Math. Comput., 218:6(2011), 2619-2630.[23] C. Zhang, H. Chen, L. Wang, Strang-type preconditioners applied to ordinary and neutral differential-algebraic equations, Numer. Linear Algebr. Appl., 18:5(2011), 843-855.[24] L. Brugnano and D. Trigiante,Convergence and stability of boundary value methods for ordinary differential equations, J. Comput. Appl. Math., 66:1-2(1996), 97-109.[25] Y. Saad, M. Schultz, GMRES:A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7:3(1986), 856-869.[26] R.H. Chan, K.N. Michael, X.Q. Jin, Strang-type preconditioners for systems of LMF-based ODE codes, IMA J. Numer. Anal., 21:2(2001), 451-462.[27] X. Jin, Developments and Applications of Block Toeplitz Iterative Solvers, Science Press, Beijing, 2006.[28] X. Jin, Preconditioning Techniques for Toeplitz Systems, Higher Education Press, Beijing, 2010. |
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