A reproducing kernel Hilbert space pseudospectral method for numerical investigation of a two-dimensional capillary formation model in tumor angiogenesis problem

In the current work, an interesting and challenging mathematical model for a two-dimensional capillary formation model in tumor angiogenesis problem will be investigated numerically. The mathematical model describes progression of tumor angiogenic factor in a unit square space domain, namely the extracellular matrix. An efficient numerical technique is performed to approximate the numerical solution of the governing practical model. The method is based on reproducing kernel Hilbert spaces in the framework of the standard pseudospectral method. Using reproducing kernel Hilbert space operational matrices and elimination the treatment of complicated boundary conditions are the main advantages of the proposed method. Some illustrative examples are included to demonstrate the effectiveness and versatility of the technique to deal with the governing mathematical model in both linear and nonlinear models .