شبیه سازی عددی پدیده نامتعارف انتشار الکترونی یون‌ها در عصب با استفاده از روش پتروف گلرکین موضعی

نویسندگان
1 دانشگاه پیام نور، دانشکدۀ علوم پایه، تهران
2 دانشگاه صنعتی مالک اشتر، مجتمع دانشگاهی علوم کاربردی
چکیده
معادله دیفرانسیلی کابل از اساسی­ترین مدل­های ریاضی در علوم عصب‌شناسی است که توصیف‌کننده پدیدۀ انتشار الکترونی یون­ها در شبکه اعصاب است. یافته­های جدید نشان می­دهد که معادله استاندارد کابل برای توصیف دقیق این پدیدۀ انتشار دارای برخی نواقص است. از این‌رو، اخیراً مدل­های ریاضی ارتقاء یافته توصیف‌کننده فرآیند، مبتنی بر نظریه حسابان کسری ارائه شده است. در این تحقیق، معادله دیفرانسیل با مشتقات کسری دوبعدی کابل غیرخطی به‌عنوان یک مدل جدید در دینامیک عصب­ها، به‌طور عددی بررسی می‌شود. یک روش محاسباتی کارا و قدرتمند که ترکیبی از روش‌های ادغام زمانی و روش بدون شبکه مبتنی بر شکل ضعیف موضعی معادله حاکم است، برای حل عددی مدل پیاده سازی و اجرا شده است. برای این منظور ابتدا یک طرح تفاضلاتی ضمنی با مرتبه دقت دو برای گسسته‌سازی مدل در جهت زمان ارائه شده است. سپس یک روش عددی بدون شبکه مبتنی بر ایده روش پتروف-گالرکین موضعی برای گسسته‌سازی کلی مسئله استفاده شده است. روش ترکیبی پیشنهادی برای حل تقریبی سه مثال اجرا شده است. نتایج عددی حاصل ارائه شده توسط جدول­ها و برخی شکل­ها کارآیی و دقت زیاد روش را نشان می­دهد.




کلیدواژه‌ها

عنوان مقاله English

A Numerical Simulation of Anomalous Electro-Diffusion of Ions in Spiny Dendrites Using a Local Petrov-Galerkin Method  

نویسندگان English

Sayyed Mahmood Zabetzadeh 1
Hadi Rohani Ghehsareh 2
1 Payame Noor university(PNU)
2 Malek Ashtar University Of Technology
چکیده English

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../files/site1/files/72/12Abstract.pdf

کلیدواژه‌ها English

Nonlinear Cable equation
Fractional differential equation
Radial basis functions
Weak form
Meshless local radial point interpolation method
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