LAUSR

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.