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A local hybrid kernel meshless method for numerical solutions of two‐dimensional fractional cable equation in neuronal dynamics
Author(s) -
Oruç Ömer
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22499
Subject(s) - regularized meshless method , mathematics , discretization , kernel (algebra) , numerical analysis , mathematical analysis , singular boundary method , finite element method , physics , combinatorics , boundary element method , thermodynamics
This study deals with obtaining numerical solutions of two‐dimensional (2D) fractional cable equation in neuronal dynamics by using a recently introduced meshless method. In solution process at first stage, time derivatives that are appeared in the considered problem are discretized by using finite difference method. Then a meshless method based on hybridization of Gaussian and cubic kernels is developed in local fashion. The problem is solved both on regular and irregular domians. L ∞ and RMS error norms are calculated and compared with other numerical methods in literature as well as exact solutions. Also, obtained condition numbers are monitored. Numerical simulations show that local hybrid kernel meshless method is a thriving method for solving 2D fractional cable equation on regular and irregular domians.