High order integrators obtained by linear combinations of symmetric-conjugate compositions

F. Casas and A. Escorihuela-Tomàs

Applied Mathematics and Computation, 2022, vol. 414, issue C

Abstract: A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic time-symmetric integrator of order 2n (n≥1). The new integrators are of order 2(n+k), k=1,2,…, and preserve time-symmetry up to order 4n+3 when applied to differential equations with real vector fields. If in addition the system is Hamiltonian and the basic scheme is symplectic, then they also preserve symplecticity up to order 4n+3. We show that these integrators are well suited for a parallel implementation, thus improving their efficiency. Methods up to order 10 based on a 4th-order integrator are built and tested in comparison with other standard procedures to increase the order of a basic scheme.

Keywords: Composition methods; Symmetric-conjugate compositions; Complex coefficients; Preservation of properties; Parabolic equations (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:414:y:2022:i:c:s0096300321007840

DOI: 10.1016/j.amc.2021.126700

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