Numerical methods for the solution of free boundary problems. (Chislennye metody resheniya zadach so svobodnoj granitsej). (Russian) Zbl 0629.65129
Moskva: Izdatel’stvo Moskovskogo Universiteta. 168 p. R. 1.50 (1987).
The main attention is paid to a description of the principal computational methods for the solution of stationary boundary problems for both second order and fourth order elliptic equations. Nonlinear resolving equations are constructed, as a rule, by using finite difference methods and by variational difference methods. On the whole two-dimensional problems are discussed. One-dimensional examples are presented in order to explain the used approaches. The solution of concrete free boundary problems illustrates the possibilities of the computational methods discussed. In a separate chapter incorrect free boundary problems are outlined.
Reviewer: I.N.Molchanov
MSC:
65Z05 | Applications to the sciences |
65N06 | Finite difference methods for boundary value problems involving PDEs |
65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |
35R25 | Ill-posed problems for PDEs |
35R35 | Free boundary problems for PDEs |
35J25 | Boundary value problems for second-order elliptic equations |
35J40 | Boundary value problems for higher-order elliptic equations |