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An \(\varepsilon \)-uniform method for a class of singularly perturbed parabolic problems with Robin boundary conditions having boundary turning point. (English) Zbl 1434.65216

Summary: A class of singularly perturbed parabolic differential equations with Robin type boundary condition having boundary turning point is propounded on a rectangular domain in the \(x\)-\(t\) plane. A numerical method comprising a standard upwind finite difference scheme is formulated on a rectangular piecewise uniform fitted mesh \(N_x \times N_t\) and it is proved to be \(\varepsilon \)-uniform. Furthermore, it is shown that the errors are bounded in the supremum norm by \(C(N_x^{- 1}(\ln N_x)^2 + N_t^{- 1})\), where \(C\) is a constant independent of \(N_x, N_t\) and the perturbation parameter \(\varepsilon \). Numerical results are given to illustrate the analytical results.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K67 Singular parabolic equations
35B25 Singular perturbations in context of PDEs
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