Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They pres

Farrell, Paul; Hegarty, Alan; Miller, John M.; O'Riordan, Eugene; Shishkin, Grigory I.

Introduction to Numerical Methods for Problems with Boundary Layers. Numerical Methods on Uniform Meshes. Layer Resolving Methods for Convection-Diffusion Problems in One Dimension. The Limitations of Non-Monotone Numerical Methods. Convection-Diffusion Problems in a Moving Medium. Convection-Diffusion Problems with Frictionless Walls. Convection-Diffusion Problems with No Slip Boundary Conditions. Experimental Estimation of Errors. Non-Monotone Methods in Two Dimensions. Linear and Nonlinear Reaction-Diffusion Problems. Prandtl Flow past a Flat Plate-Blasius' Method. Prandtl Flow past a Flat Plate-Direct Method. References.


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