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Computing the decay of a simple reversible sub-Markov semigroup. (English) Zbl 1055.65112

Summary: Two different numerical methods for solving a non-self-adjoint evolution equation are compared. If the initial function lies in the domain of the operator, a recently proposed method that combines pseudospectral ideas and semigroup theory is shown to be considerably more accurate than a standard discretization method. One example is worked out in detail, but the methods used are of much wider applicability.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K90 Abstract parabolic equations
60J22 Computational methods in Markov chains
65C40 Numerical analysis or methods applied to Markov chains
47D06 One-parameter semigroups and linear evolution equations
34L05 General spectral theory of ordinary differential operators
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References:

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