On the Computation of Blow-Up Solutions for Nonlinear Volterra Integrodifferential Equations

摘要

We make use of an adaptive numerical method to compute blow-up solutions fornonlinear ordinary Volterra integrodifferential equations (VIDEs). The methodis based on the implicit midpoint method and the implicit Euler method andis named the implicit midpoint-implicit Euler (IMIE) method and was usedto compute blow-up solutions in semilinear ODEs and parabolic PDEs in ourearlier work. We demonstrate that the method produces superior results to theadaptive PECE-implicit Euler (PECE-IE) method and the MATLAB solver ofcomparable order just as it did in our previous contribution. We use quadraturerules to approximate the integral in the VIDE and demonstrate that the choiceof quadrature rule has a significant effect on the blow-up time computed. Incases where the problem contains a convolution kernel with a singularity we useconvolution quadrature.