Numerical analysis of a stabilized Crank–Nicolson/Adams–Bashforth finite difference scheme for Allen–Cahn equations

2020 ◽  
Vol 102 ◽  
pp. 106150 ◽  
Author(s):  
Tianliang Hou ◽  
Haitao Leng
Keyword(s):  
Numerical Analysis ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Crank Nicolson

scholarly journals Discrete Symmetry Group Approach for Numerical Solution of the Heat Equation

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 359
Author(s):  
Khudija Bibi ◽  
Tooba Feroze
Keyword(s):  
Finite Difference ◽  
Heat Equation ◽  
Difference Scheme ◽  
Exact Solutions ◽  
Finite Difference Scheme ◽  
Symmetry Transformation ◽  
Discrete Symmetry ◽  
Group Approach ◽  
Comparison Of The Results ◽  
Crank Nicolson

In this article, an invariantized finite difference scheme to find the solution of the heat equation, is developed. The scheme is based on a discrete symmetry transformation. A comparison of the results obtained by the proposed scheme and the Crank Nicolson method is carried out with reference to the exact solutions. It is found that the proposed invariantized scheme for the heat equation improves the efficiency and accuracy of the existing Crank Nicolson method.

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