Singularly perturbed parabolic problems with non-smooth data

By Eugene O'Riordan, G. Shishkin. 2004

66 citations recorded by the source corpus.

In this paper, a class of singularly perturbed parabolic equations with discontinuous data is examined. Interior layers appear in the solutions of problems in this class. A numerical method is constructed for this class of problems which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter.

Subfields: Computational Theory and Mathematics, Mechanical Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c09df377ce01699bd879035baf820c644f8bc3d4

Citations in the corpus

• Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data (2018, unknown): “Now, we decompose v(x, t) by v(x, t; ε, μ) = v0(x, t) + √ εv1(x, t; ε, μ) + εv2(x, t; ε, μ), (5) where v0(x, t), v1(x, t; ε, μ) and v2(x, t; ε, μ) are the solutions of the following problems: L0v0(x, t) = f (x, t), v0(x, 0) = y(x, 0), (x, t) ∈ (Γ−∗ ∪ Γ+∗), (6) √ εL0v1(x, t) = (L0 − Lε,μ)v0(x, t), v1”
• Shishkin meshes in the numerical solution of singularly perturbed differential equations (2010, unknown): “8], problems with discontinuous data [68, 77, 78, 79] and mixed derivatives [23].”