Solving singularly perturbed problems by a weak-form integral equation with exponential trial functions

Solving singularly perturbed problems by a weak-form integral equation with exponential trial... The second-order singularly perturbed problem is transformed to a singularly perturbed parabolic type partial differential equation by using a fictitious time technique. Then we use Green’s second identity to derive a boundary integral equation in terms of the adjoint Trefftz test functions, namely a weak-form integral equation method (WFIEM). It accompanying with the exponential trial functions, which are designed to satisfy the boundary conditions automatically, can provide very accurate numerical solutions of linear and nonlinear singularly perturbed problems. For the latter problem the iterative procedure is convergent very fast. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

Solving singularly perturbed problems by a weak-form integral equation with exponential trial functions

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.02.002
Publisher site
See Article on Publisher Site

Abstract

The second-order singularly perturbed problem is transformed to a singularly perturbed parabolic type partial differential equation by using a fictitious time technique. Then we use Green’s second identity to derive a boundary integral equation in terms of the adjoint Trefftz test functions, namely a weak-form integral equation method (WFIEM). It accompanying with the exponential trial functions, which are designed to satisfy the boundary conditions automatically, can provide very accurate numerical solutions of linear and nonlinear singularly perturbed problems. For the latter problem the iterative procedure is convergent very fast.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

References

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