Abstract
We suggest an approximate method for the linear differential equation x″(t) + 2αx′ (t) + Ax(t) = f(t), where A is an unbounded self-adjoint operator, α is a given scalar and the operator A − α21 is positive semidefinite. A priori estimates of the approximation error are obtained. The results of numerical experiments for the hyperbolic equation are presented. The suggested approach can be used in the remodeling problems for complicated objects and systems if the initial mathematical model is such an equation.
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