Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2014.04.021 ◽

2014 ◽

Vol 68 (9) ◽

pp. 1071-1082 ◽

Author(s):

Michael Chapwanya ◽

Jean M.-S. Lubuma ◽

Ronald E. Mickens

Keyword(s):

Finite Difference ◽

Difference Schemes ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Positivity Preserving ◽

Cross Diffusion ◽

Nonstandard Finite Difference

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Nonstandard finite difference schemes for reaction-diffusion equations

Numerical Methods for Partial Differential Equations ◽

10.1002/(sici)1098-2426(199903)15:2<201::aid-num5>3.0.co;2-h ◽

1999 ◽

Vol 15 (2) ◽

pp. 201-214 ◽

Author(s):

Ronald E. Mickens

Keyword(s):

Finite Difference ◽

Reaction Diffusion ◽

Difference Schemes ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Nonstandard Finite Difference

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Nonstandard finite difference schemes for Michaelis-Menten type reaction-diffusion equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21733 ◽

2012 ◽

Vol 29 (1) ◽

pp. 337-360 ◽

Author(s):

Michael Chapwanya ◽

Jean M.-S. Lubuma ◽

Ronald E. Mickens

Keyword(s):

Finite Difference ◽

Reaction Diffusion ◽

Difference Schemes ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Type Reaction ◽

Nonstandard Finite Difference

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Short Note: A Note on Nonstandard Finite Difference Schemes for Reaction–Diffusion Equations Having Linear Advection

The Journal of Difference Equations and Applications ◽

10.1080/10236190410001667931 ◽

2004 ◽

Vol 10 (7) ◽

pp. 705-709 ◽

Author(s):

Mingrong Cui

Keyword(s):

Finite Difference ◽

Reaction Diffusion ◽

Difference Schemes ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Nonstandard Finite Difference

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Nonstandard finite difference schemes for reaction--diffusion equations having linear advection

Numerical Methods for Partial Differential Equations ◽

10.1002/1098-2426(200007)16:4<361::aid-num1>3.0.co;2-c ◽

2000 ◽

Vol 16 (4) ◽

pp. 361-364 ◽

Author(s):

Ronald E. Mickens

Keyword(s):

Finite Difference ◽

Reaction Diffusion ◽

Difference Schemes ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Nonstandard Finite Difference

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Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients

Computational and Applied Mathematics ◽

10.1007/s40314-021-01551-1 ◽

2021 ◽

Vol 40 (5) ◽

Author(s):

Mingrong Cui

Keyword(s):

Finite Difference ◽

Fractional Diffusion ◽

Variable Coefficients ◽

Difference Schemes ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Two Dimensional ◽

Fractional Diffusion Equations

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Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations

The Journal of Difference Equations and Applications ◽

10.1080/10236190412331334527 ◽

2005 ◽

Vol 11 (7) ◽

pp. 645-653 ◽

Author(s):

Ronald E. Mickens

Keyword(s):

Finite Difference ◽

Differential Equations ◽

Fundamental Principle ◽

Difference Schemes ◽

Dynamic Consistency ◽

Finite Difference Schemes ◽

Nonstandard Finite Difference

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Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schrödinger equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2015.1076569 ◽

2015 ◽

Vol 93 (11) ◽

pp. 1833-1844 ◽

Author(s):

A.A. Aderogba ◽

M. Chapwanya ◽

J. Djoko Kamdem ◽

J.M.-S. Lubuma

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Finite Volume ◽

Schrodinger Equation ◽

Difference Schemes ◽

Singularly Perturbed ◽

Finite Difference Schemes ◽

Nonstandard Finite Difference

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A note on second-order finite-difference schemes on uniform meshes for advection--diffusion equations

Numerical Methods for Partial Differential Equations ◽

10.1002/(sici)1098-2426(199909)15:5<581::aid-num5>3.0.co;2-m ◽

1999 ◽

Vol 15 (5) ◽

pp. 581-588 ◽

Author(s):

Daniele Funaro

Keyword(s):

Finite Difference ◽

Second Order ◽

Difference Schemes ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Advection Diffusion

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On the convergence of Mickens’ type nonstandard finite difference schemes on Lane-Emden type equations

Journal of Mathematical Chemistry ◽

10.1007/s10910-018-0880-y ◽

2018 ◽

Vol 56 (6) ◽

pp. 1667-1706 ◽

Author(s):

Amit Kumar Verma ◽

Sheerin Kayenat

Keyword(s):

Finite Difference ◽

Difference Schemes ◽

Finite Difference Schemes ◽

Nonstandard Finite Difference

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Numerical dynamics of nonstandard finite difference schemes for a computer virus propagation model

International Journal of Dynamics and Control ◽

10.1007/s40435-019-00604-y ◽

2019 ◽

Vol 8 (3) ◽

pp. 772-778 ◽

Author(s):

Quang A. Dang ◽

Manh Tuan Hoang

Keyword(s):

Finite Difference ◽

Computer Virus ◽

Difference Schemes ◽

Propagation Model ◽

Finite Difference Schemes ◽

Virus Propagation ◽

Computer Virus Propagation Model ◽

Nonstandard Finite Difference ◽

Numerical Dynamics

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