2010/02/15 by Liudmila Rozanova, Rozanova, Liudmila
Engineering · Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1002.2925
openalex publication_date 2010/02/15 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
Mathematical modeling of many physical processes such as diffusion, viscosity\nof fluids and combustion involves differential equations with small\ncoefficients of higher derivatives. These may be small diffusion coefficients\nfor modeling the spreading of impurities, small coefficients of viscosity in\nfluid flow simulation etc. The difficulty with solving such problem is that if\nyou set the small parameter at higher derivatives to zero, the solution of the\ndegenerate problem doesn't correctly approximate the original problem, even if\nthe small parameter approaches zero; the solution of the original problem\nexhibits the emergency of a boundary layer. As a result, the application of\nclassical difference schemes for solving such equations produces great\ninaccuracies. Therefore, numerical solution of differential equations with\nsmall coefficients at higher derivatives demands special difference schemes\nexhibiting uniform convergence with respect to the small parameters involved.\nIn this article author investigates two nonlinear boundary value problems on a\nfinite interval, resulting in exponential and power-law boundary layers.\n