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

摘要

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.