On difference schemes of high order of accuracy for second order evolution equations. (Russian) Zbl 0728.65053

Ashyralyev, A.

Functional-differential equations, Collect. Sci. Works, Perm’, 145-150 (1989).

[For the entire collection see Zbl 0697.00019.]
The author presents an error analysis of high order difference approximations to transient abstract problems of second order in Banach spaces. The considered approximations include Runge-Kutta methods, and Padé type schemes, which lead to three-point finite difference equations in Banach spaces.

Reviewer: R.D.Lazarov (Sofia)

MSC:

65J10	Numerical solutions to equations with linear operators
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L12	Finite difference and finite volume methods for ordinary differential equations
65L70	Error bounds for numerical methods for ordinary differential equations
34G10	Linear differential equations in abstract spaces

Keywords:

second order evolution equations; difference scheme; Padé approximations; transient abstract problems; Banach spaces; Runge-Kutta methods

Citations:

Zbl 0697.00019