Numerical analysis of a mathematical model for capillary formation in tumor angiogenesis using a meshfree method based on the radial basis function

S. Abbasbandy, H. Roohani Ghehsareh, Ishak Hashim

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

In this paper, an analysis is performed to find the numerical solution of a mathematical model for capillary formation in tumor angiogenesis. Firstly, a time stepping approach is employed for the time derivative, then a meshfree process based on a global collocation method using the radial basis functions (RBFs) is applied for solving the problem. Stability analysis of the method is investigated. Because of non-availability of the exact solutions, efficiency and accuracy of the method is demonstrated, by comparison with existing methods. Also the method is successfully applied for solving the problem with high values of the cell diffusion constant, which many of the available methods are not applicable for solving these cases.

Original languageEnglish
Pages (from-to)1811-1818
Number of pages8
JournalEngineering Analysis with Boundary Elements
Volume36
Issue number12
DOIs
Publication statusPublished - Dec 2012

Fingerprint

Angiogenesis
Meshfree Method
Radial Functions
Basis Functions
Numerical analysis
Numerical Analysis
Tumors
Tumor
Mathematical Model
Mathematical models
Derivatives
Meshfree
Time Stepping
Collocation Method
Stability Analysis
Exact Solution
Numerical Solution
Derivative
Cell

Keywords

  • Capillary formation
  • Meshfree method
  • Radial basis functions
  • Tumor angiogenesis

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics
  • Engineering(all)

Cite this

Numerical analysis of a mathematical model for capillary formation in tumor angiogenesis using a meshfree method based on the radial basis function. / Abbasbandy, S.; Roohani Ghehsareh, H.; Hashim, Ishak.

In: Engineering Analysis with Boundary Elements, Vol. 36, No. 12, 12.2012, p. 1811-1818.

Research output: Contribution to journalArticle

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