A Crank–Nicolson-type finite-difference scheme and its algorithm implementation for a nonlinear partial integro-differential equation arising from viscoelasticity

2020 ◽  
Vol 39 (4) ◽  
Author(s):  
Xuan Zheng ◽  
Hongbin Chen ◽  
Wenlin Qiu
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Integro Differential Equation ◽  
Algorithm Implementation ◽  
Crank Nicolson

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.

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