Numerical treatment of singularly perturbed two point boundary value problems using initial-value method (Q1032544)

The authors describe an initial-value method for linear and nonlinear singularly perturbed boundary value problems in the interval \([p,q]\). For linear problems, the required approximate solution is obtained by solving the reduced problem and one initial-value problem directly deduced from the given problem. For non-linear problems the original second-order nonlinear problem is linearized by using quasilinearization method. The resulting linear problem is solved by the previous method. The present method is implemented on several linear and non-linear examples which approximate the exact solution. The authors also present the approximate and exact solutions graphically.