Davies, E. B. Computing the decay of a simple reversible sub-Markov semigroup. (English) Zbl 1055.65112 LMS J. Comput. Math. 7, 1-20 (2004). 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. Cited in 1 Document 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 Keywords:pseudospectral method; Dirichlet boundary conditions; eigenvalues; eigenfunctions; reversible, sub-Markov semigroup; non-self-adjoint evolution equation PDFBibTeX XMLCite \textit{E. B. Davies}, LMS J. Comput. Math. 7, 1--20 (2004; Zbl 1055.65112) Full Text: DOI Link References: [1] Davies, J.operator Theory 43 pp 243– (2000) [2] Davies, one-parameter semigroups (1980) [3] Yosida, Functional analysis (1965) [4] DOI: 10.1017/S0962492900002932 [5] DOI: 10.1137/S0036144595295284 · Zbl 0896.15006 [6] DOI: 10.1007/s002200050521 · Zbl 0921.47060 [7] Golub, Matrix computions (1983) [8] DOI: 10.1137/S00361445024180 · Zbl 1030.65029 [9] Engel, Grad. Texts in Math. 194 (1999) [10] Hansen, SIAM Monogr. Math. Model. Comput. 4 (1997) [11] Davies, Spectral theory pp 1– (2003) [12] DOI: 10.1137/S0036139993246982 · Zbl 0811.35026 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.