A novel approach to the solution of boundary-layer problems

doi:10.1016/0196-8858(80)90004-4

Advances in Applied Mathematics

Volume 1, Issue 1, March 1980, Pages 22-36

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Abstract

By replacing a differential equation boundary-layer problem by its discrete lattice equivalent we are able to treat the resulting equation as a regular perturbation problem. We obtain the solution on the lattice as a regular perturbation series in inverse powers of the lattice spacing. To obtain the answer to the continuum problem we extrapolate the solution to the lattice problem to zero lattice spacing. This extrapolation, which is a Padé-like procedure, yields good numerical results for a wide range of problems.

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^∗: Permanent address: Department of Physics, Washington University, St. Louis, Missouri 63130.

^†: Permanent address: Department of Physics, Brown University, Providence, Rhode Island 02912.