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Solution of stiff boundary value problems by orthogonal collocation
Author(s) -
Serth R. W.
Publication year - 1975
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620090315
Subject(s) - mathematics , orthogonal collocation , singular boundary method , boundary value problem , collocation (remote sensing) , variety (cybernetics) , collocation method , singular perturbation , mathematical analysis , finite element method , computer science , ordinary differential equation , differential equation , boundary element method , engineering , structural engineering , statistics , machine learning
The utility of the method of orthogonal collocation for solving stiff boundary value problems is investigated. To this end, the method is applied to a number of very stiff problems from the engineering and applied mathematics literature. The examples include both linear and non‐linear problems defined on both finite and infinite intervals, a singular perturbation problem, and an inherently unstable problem. The examples demonstrate the usefulness of the method for a wide variety of stiff problems, as well as some of its limitations.