The method of lines for parabolic integro-differential equations

This paper introduces an efficient numerical scheme  for solving a significant class of  nonlinear parabolic integro-differential equations (PIDEs). The major contributions made in this paper are applying a direct approach based on a combination of   group preserving scheme (GPS) and  spectral meshless radial point interpolation (SMRPI) method   to transcribe the partial differential problem under study into a system of ordinary differential equations (ODEs). The resulting problem is then solved by employing the numerical method of lines, which is also a well-developed numerical method.   Two numerical experiments are carried out to evaluate the performance and effectiveness of the suggested framework.