Approximate Solution of a Parabolic Equation with the Use of a Rational Approximation to the Operator Exponential

作者：Oreshina M N^*

来源：Differential Equations, 2017, 53(3): 398-408.

DOI：10.1134/S0012266117030107

For the abstract parabolic equation x. = Bx+ bv(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.

• 出版日期2017-3