Asymptotic Numerical Solutions for Second-Order Quasilinear Singularly Perturbed Problems

For a second-order quasilinear singularly perturbed problem under the Dirichlet boundary conditions, we propose new asymptotic numerical method, which involves two problems: reduced with one-side condition and novel layer correction two-sided condition. Through introduction of variables, both problems are transformed to set three first-order initial value zero conditions. The Runge–Kutta method is then applied integrate differential equations determine unknown terminal values variables until they converge. modified solution satisfies Some examples confirm that newly proposed can achieve better problem. most perturbing parameter, present not only preserves inherent property within but also improves accuracy entire domain.