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.
Soradi Zeid, S., & Mesrizadeh, M. (2020). The method of lines for parabolic integro-differential equations. Journal of Mathematical Modeling, 8(3), 291-308. doi: 10.22124/jmm.2020.15954.1397
MLA
Samaneh Soradi Zeid; Mehdi Mesrizadeh. "The method of lines for parabolic integro-differential equations". Journal of Mathematical Modeling, 8, 3, 2020, 291-308. doi: 10.22124/jmm.2020.15954.1397
HARVARD
Soradi Zeid, S., Mesrizadeh, M. (2020). 'The method of lines for parabolic integro-differential equations', Journal of Mathematical Modeling, 8(3), pp. 291-308. doi: 10.22124/jmm.2020.15954.1397
VANCOUVER
Soradi Zeid, S., Mesrizadeh, M. The method of lines for parabolic integro-differential equations. Journal of Mathematical Modeling, 2020; 8(3): 291-308. doi: 10.22124/jmm.2020.15954.1397
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