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Mathematical modeling of many physical processes such as diffusion, viscosityof fluids and combustion involves differential equations with smallcoefficients of higher derivatives. These may be small diffusion coefficientsfor modeling the spreading of impurities, small coefficients of viscosity influid flow simulation etc. The difficulty with solving such problem is that ifyou set the small parameter at higher derivatives to zero, the solution of thedegenerate problem doesn't correctly approximate the original problem, even ifthe small parameter approaches zero; the solution of the original problemexhibits the emergency of a boundary layer. As a result, the application ofclassical difference schemes for solving such equations produces greatinaccuracies. Therefore, numerical solution of differential equations withsmall coefficients at higher derivatives demands special difference schemesexhibiting uniform convergence with respect to the small parameters involved.In this article author investigates two nonlinear boundary value problems on afinite interval, resulting in exponential and power-law boundary layers.

Construction Of Difference Schemes For Nonlinear Singular Perturbed Equations By Approximation Of Coefficients