A predictor–corrector compact finite difference scheme for Burgers’ equation

2012 ◽  
Vol 219 (3) ◽  
pp. 892-898 ◽  
Author(s):  
Pei-Guang Zhang ◽  
Jian-Ping Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Burgers Equation ◽  
Compact Finite Difference Scheme ◽  
Compact Finite Difference ◽  
Predictor Corrector

A predictor–corrector compact finite difference scheme for a nonlinear partial integro-differential equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shufang Hu ◽  
Wenlin Qiu ◽  
Hongbin Chen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Compact Finite Difference Scheme ◽  
Compact Finite Difference ◽  
Integro Differential Equation ◽  
Compact Finite Difference Method ◽  
Backward Euler ◽  
Predictor Corrector

Abstract A predictor–corrector compact finite difference scheme is proposed for a nonlinear partial integro-differential equation. In our method, the time direction is approximated by backward Euler scheme and the Riemann–Liouville (R–L) fractional integral term is treated by means of first order convolution quadrature suggested by Lubich. Meanwhile, a two-step predictor–corrector (P–C) algorithm called MacCormack method is used. A fully discrete scheme is constructed with space discretization by compact finite difference method. Numerical experiment presents the scheme is in good agreement with the theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document