On analyzing two dimensional fractional order brain tumor model based on orthonormal Bernoulli polynomials and Newton's method

被引:17
|
作者
Masti, Iman [1 ]
Sayevand, Khosro [1 ]
Jafari, Hossein [2 ]
机构
[1] Malayer Univ, Fac Math & Stat, Malayer, Iran
[2] Univ South Africa, Dept Math Sci, ZA-0003 Unisa, South Africa
关键词
Brain tumor; Operational matrix; Orthonormal Bernoulli polynomials; Fractional Caputo derivative;
D O I
10.11121/ijocta.1409
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Recently, modeling problems in various field of sciences and engineering with the help of fractional calculus has been welcomed by researchers. One of these interesting models is a brain tumor model. In this framework, a two dimensional expansion of the diffusion equation and glioma growth is considered. The analytical solution of this model is not an easy task, so in this study, a numerical approach based on the operational matrix of conventional orthonormal Bernoulli polynomials (OBPs) has been used to estimate the solution of this model. As an important advantage of the proposed method is to obtain the fractional derivative in matrix form, which makes calculations easier. Also, by using this technique, the problem under the study is converted into a system of nonlinear algebraic equations. This system is solved via Newton's method and the error analysis is presented. At the end to show the accuracy of the work, we have examined two examples and compared the numerical results with other works.
引用
收藏
页码:12 / 19
页数:8
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