A Moving Mesh Method for Mathematical Model of Capillary Formation in Tumor Angiogenesis

Using adaptive mesh methods is one of the strategies to improve numerical solutions in time-dependent partial differential equations. Moving mesh method is an adaptive mesh method. In this method, an increase in the number of mesh points is not needed for increasing the accuracy and efficiency of numerical solutions. Highly accurate solutions only can be obtained by concentrating points in areas where more accuracy is needed and decreasing the number of points in smooth areas. In this paper, moving mesh method is applied for the mathematical model of capillary formation in tumor angiogenesis. Numerical results show that this method leads to stable solutions for large values of cell diffusion coefficient in addition to enjoying necessary accuracy and efficiency.