The cubic spline finite difference for the numericalsolution of a mathematical model in the initiationangiogenesis

The numerov-spline method is proposed for a mathematical model for the rolesof endothelial, pericyte and macrophage cells in the initiation of tumor angiogenesiswith initial-boundary values. The two time-level explicit method based on the cubicspline is developed for the solution of the problem.the cubic spline has been used forapproximating the second order derivative in a space variable x and finite differencefor time variable t. The stability of proposed method is analyzed. Finally figures forendothelial, Pericyte and macrophage cells in the capillaries are presented. Numericalresults are given to examine the accuracy and efficiency of the proposed method

کلیدواژه ها:

Cubic spline ، Numerov type ، Finite difference ، Capillary formation ، Angiogenesis