Three semi-implicit compact finite difference schemes for the nonlinear partial integro-differential equation arising from viscoelasticity. (4th May 2021)

• Record Type: Journal Article
• Authors: Zheng, Xuan; Qiu, Wenlin; Chen, Hongbin
• Is Part Of: International journal of modelling & simulation. Volume 41:Number 3(2021)
• Page Start: 234
• Page End: 242
• Publication Date: 2021-05-04
• Subjects: Nonlinear partial integro-differential equation -- compact finite difference scheme -- semi-implicit scheme -- convolution quadrature -- numerical experiment; Mathematical models -- Periodicals; Simulation methods -- Periodicals; Mathematical models; Simulation methods; Periodicals; 003.3
• DOI: 10.1080/02286203.2020.1720566
• Languages: English
• ISSNs: 0228-6203

Abstract

ABSTRACT: Three semi-implicit compact finite difference schemes are described for the nonlinear partial integro-differential equation arising from viscoelasticity. In our methods, the time derivative is approximated by the backward-Euler, Crank–Nicolson-type and formally second-order backward differentiation formula scheme, respectively, and the convolution quadrature formula is employed to process the Riemann–Liouville fractional integral term. Fully discrete difference schemes are constructed with the spatial discretization by the compact finite difference formula. Meanwhile, the semi-implicit technique is used to deal with nonlinear convection term uux . In the numerical experiment, the comparisons between our methods and existing methods demonstrate the efficiency of our methods.