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For the abstract parabolic equation $$\dot x = Bx + bv\left( t \right)$$ x ˙ = B x + b v ( t ) with an unbounded self-adjoint operator B, where b is a vector and v(t) is a scalar function, we suggest a solution method based on the evaluation of some rational function of the operator B. We obtain a priori estimates of the approximation error for the output function y(t) = <x(t), l>, where l is a given vector. The results of a numerical experiment for the inhomogeneous heat equation are presented.
Differential Equations – Springer Journals
Published: Apr 18, 2017
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