Method of Rothe in evolution equations. (English) Zbl 0612.35006

Kačur, J.

Differential equations and their applications, Equadiff 6, Proc. 6th Int. Conf., Brno/Czech. 1985, Lect. Notes Math. 1192, 23-34 (1986).

[For the entire collection see Zbl 0595.00009.]
The method of Rothe is also called the method of lines or the method of semidiscretization. This is used to solve evolution problems. By using time discretization, these are approximated by corresponding elliptic problems by means of which approximate solutions to the original problems are constructed. Convergence of the approximate solutions to the solutions is also proved.

Reviewer: C.Chan

MSC:

35A35	Theoretical approximation in context of PDEs
35G10	Initial value problems for linear higher-order PDEs
35K25	Higher-order parabolic equations
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35G20	Nonlinear higher-order PDEs

Keywords:

method of Rothe; method of lines; method of semidiscretization; evolution problems; time discretization; Convergence

Citations:

Zbl 0595.00009