A SEMI-ANALYTIC METHOD FOR SOLVING SINGULARLY PERTURBED TWIN-LAYER PROBLEMS WITH A TURNING POINT

This computational study investigates a class of singularly perturbed second-order boundary-value problems having dual (twin) boundary layers and simple turning points. It is well-known that the classical discretization methods fail to resolve sharp gradients arising in solving differential equations as perturbation (diffusion) parameter decreases, i.e., ε → 0+. To this end, paper proposes semi-analytic hybrid method consisting numerical procedure based on finite differences an asymptotic called Successive Complementary Expansion Method (SCEM) approximate solution such problems. Two experiments are provided demonstrate method’s implementation evaluate its performance. Several comparisons with results existing literature also made. The observations reveal leads good profiles achieves only few iterations.