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. and 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
Soradi Zeid, S. , and Mesrizadeh, M. . "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
CHICAGO
S. Soradi Zeid and M. 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
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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