Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
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TL;DR: Four complementary asymptotic expansions are derived which approximate the incomplete gamma functions @C(a,z) and @c(a-z) for large values of their variables a and z with simpler structure than other expansions previously given in the literature.
30 citations
TL;DR: The Galerkin finite element method that uses piecewise linear functions on Shishkin- and Bakhvalov-type of meshes is applied to a linear reaction-diffusion equation with discontinuous source term is shown to be convergent, uniformly in the perturbation parameter.
Abstract: Abstract A Galerkin finite element method that uses piecewise linear functions on Shishkin- and Bakhvalov–Shishkin-type of meshes is applied to a linear reaction-diffusion equation with discontinuous source term. The method is shown to be convergent, uniformly in the perturbation parameter, of order N –2 ln2 N for the Shishkin-type mesh and N –2 for the Bakhvalov–Shishkin-type mesh, where N is the mesh size number. Numerical experiments support our theoretical results.
30 citations
TL;DR: In this article, the authors give necessary and sufficient conditions for the solutions of the differential equation (p ( t ) x "( t ))' = q (t ) x '(t ))' to be bounded together with their first derivatives.
29 citations
29 citations
TL;DR: The author summarizes the applications of matching a global and a local approximation to specific problems in the nineteenth century by a number of well-known natural philosophers, starting with Laplace in 1805.
Abstract: Ludwig Prandtl is properly credited with the development of the boundary-layer idea in viscous flow, which was generalized to the method of matched asymptotic expansions. However, the idea of matching a global and a local approximation was previously applied to specific problems in the nineteenth century by a number of well-known natural philosophers, starting with Laplace in 1805. The author summarizes their applications in hydrostatics, hydrodynamics, elasticity, electrostatics, and acoustics, with particular attention to the process of matching.
29 citations