References
- K. Aziz and A. Settari, Petroleum Reservoir Simulation, Applied Science Publisher, Ltd, London, 1979.
- J. Bear, Hydraulics of Groundwater, McGraw-Hill, New York, 1978.
- M.P. Bekakos and D.J. Evans, The double alternating group explicit method for non-linear parabolic equations on MIMD parallel computers, Parallel Comput. 18 (1992), pp. 879–895. doi: 10.1016/0167-8191(92)90034-5
- W. Chen, X. Li, and D. Liang, Energy-conserved splitting FDTD methods for Maxwell's equations, Numer. Math. 108 (2008), pp. 445–485. doi: 10.1007/s00211-007-0123-9
- A.J. Chorin and J.E. Marsdon, A Mathematical Introduction to Fluid Mechanics (Texts in Applied Mathematics), 2nd ed., Springer-Verlag, New York, 1990.
- C.N. Dawson, Q. Du, and T.F. Dupont, A finite difference domain decomposition algorithm for numerical solution of the heat equation, Math. Comput. 57 (1991), pp. 63–71. doi: 10.1090/S0025-5718-1991-1079011-4
- J. DouglasJr. and S. Kim, Improved accuracy for locally one-dimensional methods for parabolic equations, Math. Models Appl. Sci. 11 (2001), pp. 1563–1579. doi: 10.1142/S0218202501001471
- J. DouglasJr. and D. Peaceman, Numerical solution of two-dimensional heat flow problems, Am. Inst. Chem. Eng. J. 1 (1955), pp. 505–512. doi: 10.1002/aic.690010421
- C. Du and D. Liang, An efficient S-DDM iterative approach for compressible contamination fluid flows in porous media, J. Comput. Phys. 229, pp. 4501–4521.
- Q. Du, M. Mu, and Z.N. Wu, Efficient parallel algorithms for parabolic problems, SIAM J. Numer. Anal. 39 (2001), pp. 1469–1487. doi: 10.1137/S0036142900381710
- E. D'Yakonov, Difference schemes with split operators for multidimensional unsteady problems (English translation), USSR Comput. Math. 3 (1963), pp. 581–607. doi: 10.1016/0041-5553(63)90531-7
- D.J. Evans and A.R.B. Abdullah, Group explicit methods for parabolic equations, Int. J. Comput. Math. 14 (1983), pp. 73–105. doi: 10.1080/00207168308803377
- D.J. Evans and A.R.B. Abdullah, A new explicit method for the diffusion-convection equation, Comput. Math. Appl. 11 (1985), pp. 145–154. doi: 10.1016/0898-1221(85)90143-9
- R.E. Ewing (ed.), The Mathematics of Reservoir Simulation, Frontiers Applied Mathematics, Vol. 1, SIAM, Philadelphia, 1988, pp. 294–318.
- Z. Gao and S. Xie, Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations, Appl. Numer. Math. 61 (2011), pp. 593–614. doi: 10.1016/j.apnum.2010.12.004
- R.B. Kellogg, An alternating direction method for operator equations, SIAM 12 (1964), pp. 848–854.
- D. Liang, C. Du, and H. Wang, A fractional step ELLAM approach to high dimension convection diffusion problems with forward particle tracking, J. Comput. Phys. 221 (2007), pp. 198–225. doi: 10.1016/j.jcp.2006.06.022
- G. Marchuk, Methods of Numerical Mathematics, Springer-Verlag, New York, 1982.
- K. Mohanty and D.J. Evans, Alternating group explicit parallel algorithms for the solution of one-space dimensional non-linear singular parabolic equations using an O(k2+h4) difference method, Int. J. Comput. Math. 82 (2005), pp. 203–218. doi: 10.1080/00207160412331291134
- D. Peaceman and H. Racheford, The numerical solution of parabolic and elliptic equations, J. Soc. Ind. Appl. Math. 3 (1955), pp. 28–41. doi: 10.1137/0103003
- J. Qin, The new alternating direction implicit difference methods for solving three-dimensional parabolic equations, Appl. Math. Model. 34 (2010), pp. 890–897. doi: 10.1016/j.apm.2009.07.006
- F. Qu and W. Wang, Alternating segment explicit-implicit scheme for nonlinear third-order KDV equation, Appl. Math. Mech. (English) 28(7) (2007), pp. 973–980. doi: 10.1007/s10483-007-0714-y
- B.F. Smith, P.E. Bjøst, and W.D. Gropp, Domain Decomposition Methods for Partial Differential Equations, Cambridge University Press, Cambridge, 1996.
- B.-L. Zhang, G.-X. Yuan, X.-P. Liu, and J. Chen, The Parallel Finite Difference Methods for Partial differential Equation, Science Press, Beijing, 1994.