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:: Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) ::
Mathematical Researches 2021, 7(2): 0-0 Back to browse issues page
Nonlinear Cable equation, Fractional differential equation, Radial point interpolation method, Meshless local Petrov – Galerkin, Stability analysis
Sayyed Mahmood Zabetzadeh Mr 1, Hadi Rohani Ghehsareh Dr2
1- Payame Noor university(PNU) , zabetzadeh@yahoo.com
2- Malek Ashtar University Of Technology
Abstract:   (144 Views)
The cable equation is one the most fundamental mathematical models in the neuroscience, which describes the electro-diffusion of ions in denderits. New findings indicate that the standard cable equation is inadequate for describing the process of electro-diffusion of ions. So, recently, the cable model has been modified based on the theory of fractional calculus. In this paper, the two dimensional time fractional nonlinear cable equation as an improved mathematical model in neuronal dynamics, is investigated numerically. An efficient and powerful computational technique based on the combination of time integration scheme and local weak form meshfree method has been formulated and implemented to solve the underlying problem. An implicit difference scheme with second order accuracy is used to discretize the model in the temporal direction. Then a meshless method based on the local Petrov-Galerkin technique is employed to fully discretize the model. The proposed numerical technique is performed to approximate the solutions of three examples. Presented results through the Tables and figures confirm the high efficiency and accuracy of the method.
Keywords: Nonlinear Cable equation, Fractional differential equation, Radial basis functions, Weak form, Meshless local radial point interpolation method
     
Type of Study: Original Manuscript | Subject: alg
Received: 2019/05/17 | Accepted: 2019/11/9 | Published: 2021/09/1 | ePublished: 2021/09/1
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Zabetzadeh S M, Rohani Ghehsareh H. Nonlinear Cable equation, Fractional differential equation, Radial point interpolation method, Meshless local Petrov – Galerkin, Stability analysis. Mathematical Researches. 2021; 7 (2)
URL: http://mmr.khu.ac.ir/article-1-2945-en.html


Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) Back to browse issues page
پژوهش‌های ریاضی Mathematical Researches
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