A new approach for numerical solution of nonlinear singular boundary value problems arising in physiology

In this work a class of nonlinear singular ordinary differential equations, that arises in the study of various tumor growth problems, steady state oxygen diffusion in spherical cell with Michaelis-Menten uptake kinetics and the distribution of heat sources in the human head, is solved by a new method based on shifted Legendre polynomials. Operational matrices of derivatives for this function are presented to reduce the nonlinear singular boundary value problems that arise in physiology to a system of nonlinear algebraic equations. The method is computationally very simple and attractive, and applications are demonstrated through illustrative examples.