Numerical solution of a mathematical model for capillary formation in tumor angiogenesis <i>via</i> the tau method

Saadatmandi, Abbas; Dehghan, Mehdi

doi:10.1002/cnm.1045

Cited by 35 publications

(15 citation statements)

References 13 publications

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“…The main advantage of the new method over finite difference techniques is that, latter methods provide the solution of the problem on mesh points only. The method proposed in this work can be extended to solve the important nonlinear partial differential equations investigated in [37][38][39].…”

Section: Discussionmentioning

confidence: 99%

A numerical method for solving the hyperbolic telegraph equation

Dehghan

Shokri

2007

Numerical Methods Partial

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193

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Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this article, we propose a numerical scheme to solve the one-dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function. The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.

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Section: Discussionmentioning

confidence: 99%

A numerical method for solving the hyperbolic telegraph equation

Dehghan

Shokri

2007

Numerical Methods Partial

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193

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“…This method may be viewed as a special case of the so-called Petrov-Galerkin method. But, unlike the Galerkin approximation, the expansion functions are not required to satisfy the boundary constraint individually [25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 98%

Rational and Exponential Legendre Tau Method on Steady Flow of a Third Grade Fluid in a Porous Half Space

Baharifard

Kazem

Parand

2015

Int. J. Appl. Comput. Math

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In this paper, we decide to compare rational and exponential Legendre functions Tau approach to solve the governing equations for the flow of a third grade fluid in a porous half space. Firstly, we estimate an upper bound for function approximation based on mentioned functions in semi-infinite domain, and discuss that the analytical functions have a superlinear convergence for these basis. Also the operational matrices of derivative and product of these functions are presented to reduce the solution of this problem to the solution of a system of nonlinear algebraic equations. The comparison of the results of rational and exponential Legendre Tau methods with numerical solution shows the efficiency and accuracy of these methods. We also make a comparison between these two methods themselves and show that using exponential functions, leads to more accurate results and faster convergence in this problem.

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“…In addition Saadatmandi and Dehghan [22] discusses on a problem that arises in mathematical biology.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the system of nonlinear ordinary differential equations arising in kinetic modeling of lactic acid fermentation and epidemic model

Kelleci

Yıldırım

2011

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYIn this study, we introduce an efficient method for solving the kinetic modeling of lactic acid fermentation and epidemic model. First model accounts for the transient response for the cell growth, substrate utilization and lactic acid production during the fermentation process and second model is the problem of spread of a non-fatal disease in a population that is assumed to have constant size over the period of the epidemic model. We use homotopy perturbation method (HPM) to solve kinetic model for the batch production of lactic acid under submerged fermentation of cheese whey using Lactobacillus helveticus and epidemic model in a population.

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

Cited by 35 publications

References 13 publications

A numerical method for solving the hyperbolic telegraph equation

A numerical method for solving the hyperbolic telegraph equation

Rational and Exponential Legendre Tau Method on Steady Flow of a Third Grade Fluid in a Porous Half Space

Numerical solution of the system of nonlinear ordinary differential equations arising in kinetic modeling of lactic acid fermentation and epidemic model

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