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Original Articles

A new explicit method for the solution of

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Pages 325-353 | Received 01 Jun 1983, Published online: 20 Mar 2007

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X. F. Feng & Z. F. Tian. (2006) Alternating group explicit method with exponential-type for the diffusion–convection equation. International Journal of Computer Mathematics 83:10, pages 765-775.
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X. F. Feng, Z. F. Tian & S. Q. Dai. (2005) Numerical solution of the incompressible Navier–Stokes equations with exponential type schemes. International Journal of Computer Mathematics 82:9, pages 1167-1176.
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Zhang Bao-Lin, Wan Zheng-Su & D.J. Evans. (2002) A Note on the Truncation Error for the GE Scheme. International Journal of Computer Mathematics 79:9, pages 1009-1012.
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Hassan N. A. Ismail & Elsayed M. E. Elbarbary. (2001) Restrictive taylor's approximation and parabolic partial differential equations. International Journal of Computer Mathematics 78:1, pages 73-82.
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Elsayed M.E.M Elbarbary. (2001) Accelerating technique for implicit finite difference schemes for two dimensional parabolic partial differential equations. International Journal of Computer Mathematics 77:1, pages 135-144.
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HassanN.A. Ismail & ElsayedM.E. Elbarbary. (1998) Restrictive padé approximation and parabolic partial differential equations. International Journal of Computer Mathematics 66:3-4, pages 343-351.
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A. B. GUMEL, E. H. TWIZELL & M. A. ARIGU. (1997) PARALLEL L0-STABLE METHODS FOR THE MULTI-DIMENSIONAL DIFFUSION EQUATION. Parallel Algorithms and Applications 11:1-2, pages 13-25.
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A. B. Gumel, W. T. Ang & E. H. Twizell. (1997) Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of mass. International Journal of Computer Mathematics 64:1-2, pages 153-163.
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Han Zhen, Fu Hongyuan & Shen Longjun. (1994) Pure alternating block explicit-implicit method for the diffusion equation in two space dimensions. International Journal of Computer Mathematics 51:1-2, pages 81-93.
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Chen Jing & Zhang Bao-Lin. (1992) A class of alternating block crank-nicolson method. International Journal of Computer Mathematics 45:1-2, pages 89-112.
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B.J. Noye & K.J. Hayman. (1992) Explictt two-level finite-difference methods for the two-dimensional diffusion equation. International Journal of Computer Mathematics 42:3-4, pages 223-236.
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Zhang Bao-Lin & Su Xiu-Min. (1991) Alternating block explicit-implicit method for the two-dimensional diffusion equation. International Journal of Computer Mathematics 38:3-4, pages 241-255.
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D. J. Evans & M. S. Sahimi. (1989) The numerical solution of burgers' equation by the alternating group explicit (age) method. International Journal of Computer Mathematics 29:1, pages 39-64.
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A. Rahman Abdullah & D. J. Evans. (1989) Fast group explicit algorithms for diffusion problems. International Journal of Computer Mathematics 27:3-4, pages 181-197.
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Dan Wu, Junliang Lv & Hao Qian. (2022) Parallel domain decomposition schemes based on finite volume element discretization for nonsteady-state diffusion equations on distorted meshes. Computers & Mathematics with Applications 112, pages 97-115.
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Geyang Guo & Shujuan Lü. (2016) Unconditional stability of alternating difference schemes with intrinsic parallelism for two-dimensional fourth-order diffusion equation. Computers & Mathematics with Applications 71:10, pages 1944-1959.
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Qiu Yan Xu & Fuli Qu. (2012) A New Alternating Group Explicit Algorithm for Solving 2D Diffusion Equation. Applied Mechanics and Materials 263-266, pages 2301-2307.
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Norhashidah Hj. Mohd. Ali & Khoo Kok Teong. (2010) Numerical performance of parallel group explicit solvers for the solution of fourth order elliptic equations. Applied Mathematics and Computation 217:6, pages 2737-2749.
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Jie Sun & Xiao-liang Cheng. (2010) Iterative methods for a forward-backward heat equation in two-dimension. Applied Mathematics-A Journal of Chinese Universities 25:1, pages 101-111.
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Mohammad Siddique. (2009) Smoothing of Crank–Nicolson scheme for the two-dimensional diffusion with an integral condition. Applied Mathematics and Computation 214:2, pages 512-522.
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Mohammad Siddique. (2009) Smoothing of Crank-Nicolson Method for 2-D Inhomogeneous Parabolic Problems with Nonlocal Boundary Conditions. Smoothing of Crank-Nicolson Method for 2-D Inhomogeneous Parabolic Problems with Nonlocal Boundary Conditions.
Mohd Ali Norhashidah Hj.Rosni Abdullah & Jun Kok Lee. 2003. Recent Advances in Parallel Virtual Machine and Message Passing Interface. Recent Advances in Parallel Virtual Machine and Message Passing Interface 232 236 .
Zhang Bao-Lin. (2000) Difference Graphs of Block ADI Method. SIAM Journal on Numerical Analysis 38:3, pages 742-752.
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Guang-wei Yuan, Long-jun Shen & Yu-lin Zhou. (1999) Unconditional stability of alternating difference schemes with intrinsic parallelism for two-dimensional parabolic systems. Numerical Methods for Partial Differential Equations 15:6, pages 625-636.
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Baolin Zhang. (1998) Alternating difference block methods and their difference graphs. Science in China Series E: Technological Sciences 41:5, pages 482-487.
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Liu Xiao-Yu & Zhang Bao-Lin. (1996) Local one-dimensional ase-i scheme for 2D diffusion equation. Wuhan University Journal of Natural Sciences 1:3-4, pages 515-521.
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Chen Jing. (1994) Alternating block Crank-Nicolson method for the 3-D heat equation. Applied Mathematics and Computation 66:1, pages 41-61.
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Zhang Baolin & Li Wenzhi. (1994) On Alternating Segment Crank-Nicolson scheme. Parallel Computing 20:6, pages 897-902.
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G.A. Evans. (1992) Computing time-dependent eddy currents in tokamaks. Computer Physics Communications 69:2-3, pages 243-252.
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M. Carmignani, A. Genco & G. Pecorella. 1991. Applications of Supercomputers in Engineering II. Applications of Supercomputers in Engineering II 37 49 .
D.J Evans & M.S Sahimi. (1990) The solution of nonlinear parabolic partial differential equations by the alternating group explicit (AGE) method. Computer Methods in Applied Mechanics and Engineering 84:1, pages 15-42.
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B.Marques da Silva, L.A. Avaca & E.R. Gonzalez. (1989) New explicit finite difference methods in the digital simulation of electrochemical problems. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 269:1, pages 1-14.
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Daniel Zwillinger. 1989. Handbook of Differential Equations. Handbook of Differential Equations 595 650 .
B.Marques Da Silva, L.A. Avaca & E.R. González. (1988) On the use of the saul'yev algorithms in the digital simulation of electrochemical processes. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 250:2, pages 458-460.
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