Stability analysis for some numerical schemes of partial differential equation with extra measurements. (English) Zbl 1488.65378
Summary: This paper is devoted to study the stability analysis of some finite difference schemes for an inverse problem with unknowns time-dependent coefficients subject to extra measurements. We prove that the popular forward time centered space scheme is a conditional method. But the backward time centered space and Crank Nicolson methods are suitable schemes because they are unconditional methods. We justify this advantage of the stability analysis versus the some numerical methods with an example. All the results and a numerical example are in two-dimensional setting.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 82D10 | Statistical mechanics of plasmas |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35R30 | Inverse problems for PDEs |
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