@article { author = {Soradi Zeid, Samaneh and Mesrizadeh, Mehdi}, title = {The method of lines for parabolic integro-differential equations}, journal = {Journal of Mathematical Modeling}, volume = {8}, number = {3}, pages = {291-308}, year = {2020}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2020.15954.1397}, abstract = {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.}, keywords = {Parabolic integro-differential equation,partial differential equation,meshless method,radial point interpolation technique,group preserving scheme}, url = {https://jmm.guilan.ac.ir/article_4037.html}, eprint = {https://jmm.guilan.ac.ir/article_4037_6fc65daf4904bd5ada4c05abbf37e869.pdf} }