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Weighted residual solutions in the time domain
Author(s) -
Segerlind Larry J.
Publication year - 1989
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.1620280314
Subject(s) - mathematics , interpolation (computer graphics) , residual , method of mean weighted residuals , quadratic equation , ordinary differential equation , galerkin method , stability (learning theory) , weighting , linear interpolation , numerical stability , partial differential equation , mathematical analysis , differential equation , numerical analysis , finite element method , algorithm , computer science , geometry , thermodynamics , animation , medicine , physics , computer graphics (images) , radiology , machine learning , polynomial
The Galerkin and subdomain forms of the weighted residual method are used to generate recursive equations in time for the numerical solution of a system of ordinary differential equations. The single‐step methods that result from a linear interpolation equation match currently available methods whose stability and oscillation properties are known. A three‐level scheme developed by combining two linear elements is shown to be unconditionally unstable. Two of the three schemes obtained using a quadratic interpolation equation and quadratic weighting functions are also shown to be unconditionally unstable. The third scheme is unconditionally stable, but the calculated values for a numerical solution of u̇ + u = 0, u (0) = 1 are not as accurate as the values obtained using the single‐step central difference method.