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A Petrov-Galerkin approximation of convection-diffusion and reaction- diffusion problems. (English) Zbl 0748.65061
A new construction of test functions in the Petrov-Galerkin method is described. Using this construction, the author proposes algorithms for solving the Dirichlet problem for the differential equation \(-\varepsilon u''+pu'+qu=f\), where the positive number \(\varepsilon\) is supposed to be much less than the discretization step and the values of \(| p|\), \(q\).
An algorithm for the corresponding two-dimensional problem is also suggested and numerical examples are given to demonstrate the effectiveness of the proposed algorithms.
Reviewer: K.Najzar (Praha)

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations, general theory for ordinary differential equations
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