Zernike radial polynomials method for solving nonlinear singular boundary value problems arising in physiology
Subject Areas : StatisticsM.A. Ebadi 1 , E.S. Hashemizadeh 2 , A.H. Refahi Sheikhani 3
1 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
2 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
3 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
Keywords: ماتریس عملیاتی مشتق, چند جمله ای های زرنیکه شعاعی, مسائل مقدار مرزی منفرد غیر خطی,
Abstract :
The aim of this paper is to provide a new numerical method for solving nonlinear singular differential equations that arise in biology problem. These kind of problems appear in various biology problems like oxygen diffusion in red blood cells, distribution of heat source in human head and cancer tumor growth and etc. In this paper this equations are solved by a new numerical method by using Zernike radial polynomials. In the proposed method for the first time the operational matrix of derivative for Zernike radial polynomials is derived and by using this operational matrices of derivative of Zernike radial functions the differential equation convert to a system of algebraic equations that can be solved easily. The implementation of this proposed method is simple and attractive. Finally some applied models are presented to compare the results by other method results, and they show the accuracy and efficiency of the presented method.
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