A predictor-corrector method for fractional evolution equations

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참고문헌 (17)

1. K. Adolfsson, "Adaptive discretization of fractional order viscoelasticity using sparse time history", Comput. Methods Appl. Mech. Engrg, 193(42-44), pp.4567~4590 (2004)
2. B. Baeumer, "Fractional reproduction-dispersal equa-tions and heavy tail dispersal kernels", Bull. Math. Biol, 69(7), pp.2281~2297 (2007)
3. Z. Chen, "Finite Element Methods and Their Applications" (2005), Springer Verlag
4. 최홍원, "NUMERICAL SOLUTIONS FOR SPACE FRACTIONAL DISPERSION EQUATIONS WITH NONLINEAR SOURCE TERMS", 대한수학회보, 47(6), pp.1225~1234 (2010), 대한수학회
5. Y. J. Choi, "Finite element solutions for the space fractional diffusion equations with a nonlinear source term", Abstr. Appl. Anal, 2012, pp.25~ (2012)
6. Z. Q. Deng, "Numerical solution of fractional advection-dispersion equation", J. Hydraulic Engineering, 130, pp.422~431 (2004)
7. K. Diethlem, "A predictor-corrector approach for the nu-merical solution of fractional differential equations", Nonlinear Dynam, 29(1-4), pp.3~22 (2002)
8. V. J. Ervin, "Numerical approximation of a time dependent, nonlinear space-fractional diffusion equation", SIAM J. Numer. Anal, 45(2), pp.572~591 (2007)
9. Matt G. Herrick, "Hydraulic conductivity, velocity, and the order of the fractional dispersion derivative in a highly heterogeneous system", Water Resources Research, 38(11), pp.9-1~9-13 (2002), Wiley-Blackwell[DOI]
10. F. Liu, "Numerical solution of the space fractional Fokker-Planck equation", J. Comput. Appl. Math, 166(1), pp.209~219 (2004)
11. V. E. Lynch, "Numerical methods for the solution of partial differential equations of fractional order", J. Comput. Phys, 192(2), pp.406~421 (2003)
12. M. M. Meerschaert, "Finite difference methods for two-dimensional fractional dispersion equation", J. Comput. Phys, 211(1), pp.249~261 (2006)
13. M. M. Meerschaert, "Finite difference approximations for fractional advection-dispersion flow equations", J. Comput. Appl. Math, 172(1), pp.65~77 (2004)
14. M. M. Meerschaert, "Finite difference approximations for two-sided space-fractional partial differen-tial equations", Appl. Numer. Math, 56(1), pp.80~90 (2006)
15. K. B. Oldham, "The Fractional Calculus" (2002), Dover Publications
16. J. P. Roop, "Computational aspects of FEM approximation of fractional advection dis-persion equations on bounded domains in R2", J. Comput. Appl. Math, 193(1), pp.243~268 (2006)
17. C. Tadjeran, "A second-order accurate numerical approximation for the fractional diffusion equation", J. Comput. Phys, 213(1), pp.205~213 (2006)