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Numerical simulation of a generalized anomalous electro‐diffusion process in nerve cells by a localized meshless approach in Pseudospectral mode
Author(s) -
Roohani Ghehsareh Hadi,
Seidzadeh Maryam Sadat,
Etesami Seyed Kamal
Publication year - 2020
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2756
Subject(s) - discretization , pseudospectral optimal control , pseudo spectral method , interpolation (computer graphics) , mathematics , nonlinear system , algebraic equation , mathematical analysis , mathematical optimization , computer science , fourier transform , physics , animation , fourier analysis , computer graphics (images) , quantum mechanics
Abstract Pseudospectral techniques are known as powerful tools and highly accurate solvers to deal with partial differential equations. In the current work, a local meshless technique in Pseudospectral mode is employed to deal with an interesting and general mathematical model which describes anomalous electrodiffusion of ions in spiny dendrites, the two‐dimensional variable‐order time fractional nonlinear cable equation. For this purpose, at first step a second‐order implicit difference method and a modified second‐order weighted and shifted Grünwald difference scheme are used to discretize the appearing integer and variable order fractional time derivatives, respectively. Then a local Pseudospectral meshless method based on the sufficiently smooth compactly supported radial point interpolation basis functions is formulated for solving the semidiscretized problem. The main advantage of the proposed computational technique is that it leads to a sparse and better‐conditioned system of algebraic equations. Finally, some numerical experiments are presented to demonstrate and verify the performance and accuracy of the method.