Cubic spline for a class of non-linear singular boundary value problems arising in physiology

Cubic spline method to analyze a class of non-linear singular boundary value problems defined byy″(x)+mxy′=f(x,y),y′(0)=0,αy(1)+βy′(1)=γis presented. The quesilinearization technique is used to reduce the given non-linear problem to a sequence of linear problems. The resulting set of differential equations are modified at the singular point and are treated by using cubic spline for finding the numerical solution. The numerical method is tested for its efficiency by considering two examples from physiology.