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Original Articles

Explictt two-level finite-difference methods for the two-dimensional diffusion equation

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Pages 223-236 | Received 19 Aug 1991, Published online: 19 Mar 2007

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Mehdi Dehghan. (2001) Numerical methods for two-dimensional parabolic inverse problem with energy overspecification. International Journal of Computer Mathematics 77:3, pages 441-455.
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Mehdi Dehghan. (2000) Finite difference schemes for two-dimensional parabolic inverse problem with temperature overspecification. International Journal of Computer Mathematics 75:3, pages 339-349.
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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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B. J. Noye & K. J. Hayman. (1994) New lod and adi methods for the two-dimensional diffusion equation. International Journal of Computer Mathematics 51:3-4, pages 215-228.
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B. J. Noye & K. J. Hayman. (1993) Implicit two-level finite-difference methods for the two-dimensional diffusion equation. International Journal of Computer Mathematics 48:3-4, pages 219-227.
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Hammad Khalil, Murad Khalil, Ishak Hashim & Praveen Agarwal. (2021) Extension of Operational Matrix Technique for the Solution of Nonlinear System of Caputo Fractional Differential Equations Subjected to Integral Type Boundary Constrains. Entropy 23:9, pages 1154.
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Hammad Khalil, Ishak Hashim, Waqar Ahmad Khan & Abuzar Ghaffari. (2021) A Novel Method for Solution of Fractional Order Two-Dimensional Nonlocal Heat Conduction Phenomena. Mathematical Problems in Engineering 2021, pages 1-17.
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Ömer Oruç. (2019) A Meshfree Computational Approach Based on Multiple-Scale Pascal Polynomials for Numerical Solution of a 2D Elliptic Problem with Nonlocal Boundary Conditions. International Journal of Computational Methods 17:10, pages 1950080.
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Hammad Khalil, Rahmat Ali Khan, Dumitru Baleanu & Mohammad Mehdi Rashidi. (2019) Some new operational matrices and its application to fractional order Poisson equations with integral type boundary constrains. Computers & Mathematics with Applications 78:6, pages 1826-1837.
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Hammad Khalil, Rahmat Ali Khan, Dumitru Baleanu & Samir H Saker. (2016) Approximate solution of linear and nonlinear fractional differential equations under m-point local and nonlocal boundary conditions. Advances in Difference Equations 2016:1.
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Siraj-ul-Islam, Imran Aziz & Masood Ahmad. (2015) Numerical solution of two-dimensional elliptic PDEs with nonlocal boundary conditions. Computers & Mathematics with Applications 69:3, pages 180-205.
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Ahmed Cheniguel. 2014. Transactions on Engineering Technologies. Transactions on Engineering Technologies 579 597 .
Wenyuan Liao. (2012) A high‐order ADI finite difference scheme for a 3D reaction‐diffusion equation with neumann boundary condition. Numerical Methods for Partial Differential Equations 29:3, pages 778-798.
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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.
Yuan Lin, Xuejun Gao & MingQing Xiao. (2008) A high‐order finite difference method for 1D nonhomogeneous heat equations. Numerical Methods for Partial Differential Equations 25:2, pages 327-346.
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Juliette A. Woods, Michael D. Teubner, Craig T. Simmons & Kumar A. Narayan. (2003) Numerical error in groundwater flow and solute transport simulation. Water Resources Research 39:6.
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W. F. Spotz & G. F. Carey. (2001) Extension of high-order compact schemes to time-dependent problems. Numerical Methods for Partial Differential Equations 17:6, pages 657-672.
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B. J. Noye & M. Dehghan. (1999) New explicit finite difference schemes for two-dimensional diffusion subject to specification of mass. Numerical Methods for Partial Differential Equations 15:4, pages 521-534.
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B.J. Noye & M. Dehghan. (1994) Explicit solution of two-dimensional diffusion subject to specification of mass. Mathematics and Computers in Simulation 37:1, pages 37-45.
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B.J Noye, M Dehghan & J van der Hoek. (1994) Explicit finite difference methods for two-dimensional diffusion with a non-local boundary condition. International Journal of Engineering Science 32:11, pages 1829-1834.
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