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Approximate solution of second order differential equation with unbounded operator coefficient. (Ukrainian. English summary) Zbl 1064.65519

Summary: An initial value problem for the second order differential equation with unbounded operator coefficient in Hilbert space is considered. An approximate solution of the initial problem is given by means of the quadrature collocation method for discretization of operator coefficient and the Cayley transform for the approximation error for discretization on time variable. We have established an estimate for the approximation error for the fully discreet approximation of the initial problem which automatically depends on smoothness of solution.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34G10 Linear differential equations in abstract spaces
65L70 Error bounds for numerical methods for ordinary differential equations
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