A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions

Journal of Computational Physics ◽

10.1016/j.jcp.2011.12.028 ◽

2012 ◽

Vol 231 (7) ◽

pp. 2865-2879 ◽

Author(s):

Guang-hua Gao ◽

Zhi-zhong Sun ◽

Ya-nan Zhang

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Unbounded Domain ◽

Finite Difference Scheme ◽

Diffusion Equations ◽

Artificial Boundary ◽

Artificial Boundary Conditions

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The finite difference scheme for nonlinear Schrödinger equations on unbounded domain by artificial boundary conditions

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.02.005 ◽

2018 ◽

Vol 128 ◽

pp. 183-204 ◽

Author(s):

Bo Wang ◽

Dong Liang

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Unbounded Domain ◽

Finite Difference Scheme ◽

Nonlinear Schrödinger Equations ◽

Schrödinger Equations ◽

Artificial Boundary ◽

Artificial Boundary Conditions ◽

Nonlinear Schrodinger Equations

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A new stable finite difference scheme and its error analysis for two‐dimensional singularly perturbed convection–diffusion equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22732 ◽

2020 ◽

Author(s):

Kamalesh Kumar ◽

Pramod Chakravarthy Podila

Keyword(s):

Finite Difference ◽

Error Analysis ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Singularly Perturbed ◽

Diffusion Equations ◽

Two Dimensional ◽

Convection Diffusion

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A second-order accurate finite difference scheme for a class of nonlocal parabolic equations with natural boundary conditions

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(96)00097-0 ◽

1996 ◽

Vol 76 (1-2) ◽

pp. 137-146 ◽

Author(s):

Zhi-Zhong Sun

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Parabolic Equations ◽

Finite Difference Scheme ◽

Second Order ◽

Natural Boundary ◽

Nonlocal Parabolic Equations ◽

Natural Boundary Conditions

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An Accurate Multi-level Finite Difference Scheme for 1D Diffusion Equations Derived from the Lattice Boltzmann Method

Journal of Statistical Physics ◽

10.1007/s10955-010-0004-y ◽

2010 ◽

Vol 140 (3) ◽

pp. 494-503 ◽

Author(s):

Shinsuke Suga

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Finite Difference Scheme ◽

Diffusion Equations ◽

Multi Level ◽

Boltzmann Method

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Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions

PLoS ONE ◽

10.1371/journal.pone.0206235 ◽

2018 ◽

Vol 13 (10) ◽

pp. e0206235 ◽

Author(s):

Vyacheslav A. Trofimov ◽

Evgeny M. Trykin

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Difference Schemes ◽

Finite Difference Schemes ◽

Artificial Boundary ◽

Artificial Boundary Conditions ◽

Rosenbrock Method ◽

Implicit Finite Difference

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A finite difference scheme for semilinear space-fractional diffusion equations with time delay

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.11.071 ◽

2016 ◽

Vol 275 ◽

pp. 238-254 ◽

Author(s):

Zhaopeng Hao ◽

Kai Fan ◽

Wanrong Cao ◽

Zhizhong Sun

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Semilinear Space

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A Linearized Finite Difference Scheme for the Richards Equation Under Variable-Flux Boundary Conditions

Journal of Scientific Computing ◽

10.1007/s10915-020-01196-y ◽

2020 ◽

Vol 83 (1) ◽

Author(s):

Liu Fengnan ◽

Yasuhide Fukumoto ◽

Xiaopeng Zhao

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Richards Equation ◽

Flux Boundary Conditions ◽

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On the Stability of a Weighted Finite Difference Scheme for Hyperbolic Equation with Integral Boundary Conditions

Lecture Notes in Computational Science and Engineering - Numerical Mathematics and Advanced Applications ENUMATH 2015 ◽

10.1007/978-3-319-39929-4_59 ◽

2016 ◽

pp. 617-626

Author(s):

Jurij Novickij ◽

Artūras Štikonas ◽

Agnė Skučaitė

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Hyperbolic Equation ◽

Finite Difference Scheme ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

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A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in(1+1)D

Journal of Computational Physics ◽

10.1016/j.jcp.2013.09.022 ◽

2014 ◽

Vol 256 ◽

pp. 728-747 ◽

Author(s):

René Hammer ◽

Walter Pötz ◽

Anton Arnold

Keyword(s):

Dirac Equation ◽

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Transparent Boundary Conditions

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Analysis of an upwind finite-difference scheme for a system of coupled singularly perturbed convection-diffusion equations

Computing ◽

10.1007/s00607-006-0215-x ◽

2006 ◽

Vol 79 (1) ◽

pp. 23-32 ◽

Author(s):

T. Linß

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Singularly Perturbed ◽

Diffusion Equations ◽

Convection Diffusion ◽

Upwind Finite Difference

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