Difference schemes for the solution of inverse probelms in mathematical physics. (Russian) Zbl 0958.65099
Makarov, I. M. (ed.), Fundamental principles of mathematical modelling. Moskva: Nauka. Kibernetika: Neogranichennye Vozmozhnosti i Vozmozhnye Ogranicheniya. 5-97 (1997).
This paper deals with the numerical solution of inverse problems in mathematical physics (evolution equations of the first- and second-order, parabolic partial differential equations of the second-order, boundary value problems, initial value problems). Some stability conditions for two- and three-level difference schemes are presented. The authors construct regularized schemes as a generally approach of higher quality of difference schemes. Also unconditionally stable schemes for noncorrect problems are constructed. Convergence of finite difference solutions is analyzed.
The paper introduces related important ideas associated with the analysis of numerical methods for some partial differential equations. The text would be suitable for advanced graduate courses in mathematics.
For the entire collection see [Zbl 0880.00024].
The paper introduces related important ideas associated with the analysis of numerical methods for some partial differential equations. The text would be suitable for advanced graduate courses in mathematics.
For the entire collection see [Zbl 0880.00024].
Reviewer: Pavol Chocholatý (Bratislava)
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35R30 | Inverse problems for PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 35L40 | First-order hyperbolic systems |
