High-order compact difference scheme of 1D nonlinear degenerate convection–reaction–diffusion equation with adaptive algorithm

2019 ◽  
Vol 75 (1) ◽  
pp. 43-66 ◽  
Author(s):  
Xiaoliang Zhu ◽  
Hongxing Rui
Keyword(s):  
Diffusion Equation ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Reaction Diffusion ◽  
High Order ◽  
Reaction Diffusion Equation ◽  
Compact Difference Scheme ◽  
Compact Difference ◽  
Nonlinear Degenerate

Direct calculation of waves in fluid flows using high-order compact difference scheme

AIAA Journal ◽  
1994 ◽  
Vol 32 (9) ◽  
pp. 1766-1773 ◽  
Author(s):  
Sheng-Tao Yu ◽  
Lennart S. Hultgren ◽  
Nan-Suey Liu
Keyword(s):  
Difference Scheme ◽  
Fluid Flows ◽  
Direct Calculation ◽  
High Order ◽  
Compact Difference Scheme ◽  
Compact Difference

scholarly journals A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaozhong Yang ◽  
Xu Dang
Keyword(s):  
Parallel Computing ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Reaction Diffusion ◽  
Difference Schemes ◽  
Reaction Diffusion Equation ◽  
Stability And Convergence ◽  
Parallel Difference ◽  
Fractional Reaction ◽  
Crank Nicolson

Abstract The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this paper, we propose a parallel computing method of mixed difference scheme for time fractional reaction–diffusion equation and construct a class of improved alternating segment Crank–Nicolson (IASC–N) difference schemes. The class of parallel difference schemes constructed in this paper, based on the classical Crank–Nicolson (C–N) scheme and classical explicit and implicit schemes, combines with alternating segment techniques. We illustrate the unique existence, unconditional stability, and convergence of the parallel difference scheme solution theoretically. Numerical experiments verify the theoretical analysis, which shows that the IASC–N scheme has second order spatial accuracy and $2-\alpha $ 2 − α order temporal accuracy, and the computational efficiency is greatly improved compared with the implicit scheme and C–N scheme. The IASC–N scheme has ideal computation accuracy and obvious parallel computing properties, showing that the IASC–N parallel difference method is effective for solving time fractional reaction–diffusion equation.

scholarly journals High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Yongbin Ge
Keyword(s):  
Difference Scheme ◽  
Multigrid Method ◽  
Elliptic Problems ◽  
High Order ◽  
Compact Difference Scheme ◽  
Central Difference ◽  
Present Scheme ◽  
Compact Difference ◽  
Compact Approximations ◽  
Error Terms

A high-order compact difference scheme for solving the two-dimensional (2D) elliptic problems is proposed by including compact approximations to the leading truncation error terms of the central difference scheme. A multigrid method is employed to overcome the difficulties caused by conventional iterative methods when they are used to solve the linear algebraic system arising from the high-order compact scheme. Numerical experiments are conducted to test the accuracy and efficiency of the present method. The computed results indicate that the present scheme achieves the fourth-order accuracy and the effect of the multigrid method for accelerating the convergence speed is significant.

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