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Rational Krylov methods for functions of matrices with applications to fractional partial differential equations. (English) Zbl 1452.65201

Summary: In this paper we propose a new choice of poles to define reliable rational Krylov methods. These methods are used for approximating function of positive definite matrices. In particular, the fractional power and the fractional resolvent are considered because of their importance in the numerical solution of fractional partial differential equations. The numerical experiments on some fractional partial differential equation models confirm that the proposed approach is promising.

MSC:

65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65F60 Numerical computation of matrix exponential and similar matrix functions

Software:

FEniCS; na20; RKToolbox; FiPy
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References:

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