A meshless technique based on the local radial basis functions collocation method for solving parabolic-parabolic Patlak-Keller-Segel chemotaxis model

Mehdi Dehghan; Mostafa Abbaszadeh; Akbar Mohebbi

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A meshless technique based on the local radial basis functions collocation method for solving parabolic-parabolic Patlak-Keller-Segel chemotaxis model

机译：基于局部径向基函数配置法的无网格技术求解抛物线-抛物线型Patlak-Keller-Segel趋化模型

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In this paper local radial basis functions (LRBFs) collocation method is proposed for solving the (Patlak-) Keller-Segel model. We use the Crank-Nicolson difference scheme for the time derivative to obtain a finite difference scheme with respect to the time variable for the Keller-Segel model. Then we use the local radial basis functions (LRBFs) collocation method to approximate the spatial derivative. We obtain the numerical results for the mentioned model. As we know, recently some approaches presented for preventing the blow up of the cell density. In the current paper we use the multiquadric (MQ) radial basis function. The aim of this paper is to show that the meshless methods based on the local RBFs collocation approach are also suitable for solving models that have the blow up of the cell density. Also, six test problems are given that show the acceptable accuracy and efficiency of the proposed schemes.

机译：本文提出了局部径向基函数（LRBFs）配置方法来求解（Patlak-）Keller-Segel模型。对于时间导数，我们使用Crank-Nicolson差分方案，以获得关于Keller-Segel模型的时间变量的有限差分方案。然后，我们使用局部径向基函数（LRBF）配置方法来近似空间导数。我们获得上述模型的数值结果。众所周知，最近提出了一些防止细胞密度爆炸的方法。在当前论文中，我们使用多二次方（MQ）径向基函数。本文的目的是表明基于局部RBF搭配方法的无网格方法也适用于求解细胞密度爆炸的模型。此外，给出了六个测试问题，这些问题表明了所提出方案的可接受的准确性和效率。

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来源
《Engineering analysis with boundary elements》 |2015年第7期|129-144|共16页
作者
Mehdi Dehghan; Mostafa Abbaszadeh; Akbar Mohebbi;
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作者单位

Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, 15914 Tehran, Iran;

Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, 15914 Tehran, Iran;

Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Keller-Segel model; Nonlinear equation; Kansa's approach; Radial basis functions (RBFs); Local collocation meshless method; Patlak-Keller-Segel chemotaxis model;

机译：Keller-Segel模型;非线性方程Kansa的方法;径向基函数（RBF）;局部搭配无网格法;Patlak-Keller-Segel趋化模型;

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1. Applying the Method of Characteristics and the Meshless Localized Radial Basis Function Collocation Method to Solve Shallow Water Equations [J] . Hsiang C. C., Chou C. K., Young D. L., Journal of Engineering Mechanics . 2018,第7期

机译：应用特征方法和无网局部径向基函数搭配方法解决浅水方程
2. The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrodinger equation arising in quantum mechanics [J] . Akbar Mohebbi, Mostafa Abbaszadeh, Mehdi Dehghan Engineering analysis with boundary elements . 2013,第2期

机译：使用基于搭配和径向基函数的无网格技术求解量子力学中出现的时间分数非线性Schrodinger方程
3. Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions [J] . Guangming Yao, Siraj-ul-Islam, Bozidar Sarler Engineering analysis with boundary elements . 2012,第11期

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4. Least-Squares Collocation Points Meshless Method with Radial Basis Functions Solving Elliptic Equations [C] . Baoshan Miao, Xinqiang Qin, Gang Hu, ISAI 2010;International conference on information security and artificial intelligence . 2010

机译：径向基函数的最小二乘配点无网格方法求解椭圆方程
5. Accelerating the performance of a novel meshless method based on collocation with radial basis functions by employing a graphical processing unit as a parallel coprocessor. [D] . Owusu-Banson, Derek. 2012

机译：通过将图形处理单元用作并行协处理器，加速了基于新的基于径向和功能并置的无网格方法的性能。
6. Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method [O] . Shu-Bo Chen, Samaneh Soradi-Zeid, Hadi Jahanshahi, 2020

机译：通过径向基函数和搭配方法的关节应用优化时滞分数方程的最佳控制
7. A meshless collocation method based on radial basis functions and wavelets [O] . Ho, SL, Yang, S, Wong, HCC, 2004

机译：基于径向基函数和小波的无网格配置方法
8. A Meshless Method Using Radial Basis Functions for Beam Bending Problems [R] . Raju, I. S., Phillips, D. R., Krishnamurthy, T. 2004

机译：基于径向基函数的无网格梁弯曲问题

A meshless technique based on the local radial basis functions collocation method for solving parabolic-parabolic Patlak-Keller-Segel chemotaxis model

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