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An error analysis of the tau method for a class of singularly perturbed problems for differential equations
Author(s) -
Ortiz E. L.,
PhamNgocDinh A.,
Törnig W.
Publication year - 1984
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670060128
Subject(s) - mathematics , uniqueness , class (philosophy) , finite element method , differential equation , error analysis , simple (philosophy) , mathematical analysis , numerical analysis , computer science , philosophy , physics , epistemology , artificial intelligence , thermodynamics
By using classical results of Poincaré and Birkhoff we discuss the existence and uniqueness of solution for a class of singularly perturbed problems for differential equations. The Tau method formulation of Ortiz [6] is applied to the construction of approximate solutions of these problems. Sharp error bounds are deduced. These error bounds are applied to the discussions of a model problem, a simple one‐dimensional analogue of Navier‐Stokes equation, which has been considered recently by several authors (see [2], [3], [8], [10]). Numerical results for this problem [8] show that the Tau method leads to more accurate approximations than specially designed finite difference or finite element schemes.