Continuous and numerical analysis of a boundary shock problem. (English) Zbl 0678.65062
A quasilinear singularly perturbed boundary value problem whose solution has a shock layer is studied. Estimates of the derivatives of the solution are derived and based on them a new independent variable is introduced. The transformed problem is then solved by the finite- difference method. The transformation corresponds to solving the original problem on a mesh which is dense in the layer. Linear convergence uniform in the perturbation parameter is proved in the discrete \(L^ 1\) norm. Numerical results show uniform pointwise convergence also.
Reviewer: V.P.Tyagi
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 34E15 | Singular perturbations for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
boundary shock problem; uniform convergence; numerical example; quasilinear singularly perturbed boundary value problem; shock layer; finite-difference method; pointwise convergenceReferences:
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