Bibliographic Details
| Title: |
Low rank Runge–Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise |
| Authors: |
Burrage, Kevin1,2, Burrage, Pamela M.3 pamela.burrage@qut.edu.au |
| Source: |
Journal of Computational & Applied Mathematics. Oct2012, Vol. 236 Issue 16, p3920-3930. 11p. |
| Subjects: |
Runge-Kutta formulas, Stochastic analysis, Hamiltonian systems, Performance evaluation, Numerical analysis, Mathematical analysis |
| Abstract: |
Abstract: In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM () methods to construct symplectic Runge–Kutta methods for all values of and with . However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge–Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
