A high-order ADI finite difference scheme for a 3D reaction-diffusion equation with neumann boundary condition

2012 ◽  
Vol 29 (3) ◽  
pp. 778-798 ◽  
Author(s):  
Wenyuan Liao
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
High Order ◽  
Reaction Diffusion Equation

A Nonstandard Finite Difference Scheme for the Reaction Diffusion Equation

2012 ◽  
Vol 166-169 ◽  
pp. 3265-3268
Author(s):  
Ming Ding Liu
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Reaction Diffusion ◽  
Discrete Models ◽  
Reaction Diffusion Equation ◽  
Nonstandard Finite Difference Scheme ◽  
Advection Term ◽  
Nonstandard Finite Difference

We use the nonstandard finite difference (NSFD) method to construct discrete models of the reaction diffusion equation. A nonstandard finite difference scheme for the reaction-diffusion equation is given. We demonstrated that the space denominator function can be based on the use of a transformation from the simple expression (Δx)2to an 4C(sin[(1/C)1/2((Δx)/2)])2.which is clearly valid for sufficiently small Δx. Another important class for which this method keeps the equation solutions are positivity and can be applied is those PDE's without advection term.

scholarly journals A Laplace transform finite difference scheme for the Fisher-KPP equation

2021 ◽  
Vol 15 ◽  
pp. 174830262199958
Author(s):  
Colin L Defreitas ◽  
Steve J Kane
Keyword(s):  
Finite Difference ◽  
Laplace Transform ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Finite Difference Methods ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Travelling Wave ◽  
Reaction Diffusion Equation ◽  
Kpp Equation

This paper proposes a numerical approach to the solution of the Fisher-KPP reaction-diffusion equation in which the space variable is developed using a purely finite difference scheme and the time development is obtained using a hybrid Laplace Transform Finite Difference Method (LTFDM). The travelling wave solutions usually associated with the Fisher-KPP equation are, in general, not deemed suitable for treatment using Fourier or Laplace transform numerical methods. However, we were able to obtain accurate results when some degree of time discretisation is inbuilt into the process. While this means that the advantage of using the Laplace transform to obtain solutions for any time t is not fully exploited, the method does allow for considerably larger time steps than is otherwise possible for finite-difference methods.

scholarly journals Adaptive High-Order Finite Difference Analysis of 2D Quenching-Type Convection-Reaction-Diffusion Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Xiaoliang Zhu ◽  
Yongbin Ge
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Reaction Diffusion ◽  
Taylor Series Expansion ◽  
Correction Method ◽  
Reaction Diffusion Equation ◽  
Spatial Derivative ◽  
Central Difference ◽  
Forward Difference

Quenching characteristics based on the two-dimensional (2D) nonlinear unsteady convection-reaction-diffusion equation are creatively researched. The study develops a 2D compact finite difference scheme constructed by using the first and the second central difference operator to approximate the first-order and the second-order spatial derivative, Taylor series expansion rule, and the reminder-correction method to approximate the three-order and the four-order spatial derivative, respectively, and the forward difference scheme to discretize temporal derivative, which brings the accuracy resulted meanwhile. Influences of degenerate parameter, convection parameter, and the length of the rectangle definition domain on quenching behaviors and performances of special quenching cases are discussed and evaluated by using the proposed scheme on the adaptive grid. It is feasible for the paper to offer potential support for further research on quenching problem.

Sign in / Sign up

Export Citation Format

Share Document