Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method.

*(English)*Zbl 1151.92017Summary: A numerical procedure is developed to obtain the solution of a mathematical model for capillary formation in tumor angiogenesis. The proposed method is based on the shifted Legendre tau technique. Our approach consists of reducing the problem to a set of algebraic equations by expanding the approximate solution as a shifted Legendre polynomial with unknown coefficients. The operational matrices of integrals and derivatives together with the tau method are then utilized to evaluate the unknown coefficients of shifted Legendre polynomials. An illustrative example is included to demonstrate the validity and applicability of the presented technique.

##### MSC:

92C50 | Medical applications (general) |

65C20 | Probabilistic models, generic numerical methods in probability and statistics |

35K20 | Initial-boundary value problems for second-order parabolic equations |

35K15 | Initial value problems for second-order parabolic equations |

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

##### Keywords:

numerical solutions; shifted Legendre tau method; capillary formation; tumor angiogenesis; operational matrix
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\textit{A. Saadatmandi} and \textit{M. Dehghan}, Commun. Numer. Methods Eng. 24, No. 11, 1467--1474 (2008; Zbl 1151.92017)

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##### References:

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