Numerical Solution of Singularly Perturbed Non-Linear Two Point Boundary Value Problems by Spline in Compression

Singularly perturbed nonlinear two point boundary value problems are considered. The original nonlinear equation is linearized using quasilinearization. Difference schemes are derived for linear case using spline in compression and are used to solve each linear equation obtained via quasilinearization. Second order uniform convergence is achieved. Numerical examples are given in support of the theoretical results.