Name
Title | ||
|---|---|---|
Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes. |
Abstract | ||
|---|---|---|
We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating point arithmetic, the precision of the results is limited by round-off error propagation. We claim that our implementation with fixed point iteration is near-optimal with respect to round-off error propagation under the assumption that the function that evaluates the right-hand side of the differential equations is implemented with machine numbers (of the prescribed floating point arithmetic) as input and output. In addition, we present a simple procedure to estimate the round-off error propagation by means of a slightly less precise second numerical integration. Some numerical experiments are reported to illustrate the round-off error propagation properties of the proposed implementation. |
Year | DOI | Venue |
|---|---|---|
2017 | https://doi.org/10.1007/s11075-017-0287-z | Numerical Algorithms |
Keywords | Field | DocType |
Symplectic implicit Runge-Kutta methods,Fixed-point iteration,Stopping criterion,Round-off errors | Runge–Kutta methods,Differential equation,Mathematical optimization,Propagation of uncertainty,Floating point,Mathematical analysis,Round-off error,Fixed-point iteration,Numerical integration,Symplectic geometry,Algorithm,Mathematics | Journal |
Volume | Issue | ISSN |
76 | 4 | 1017-1398 |
Citations | PageRank | References |
4 | 0.63 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mikel Antoñana | 1 | 5 | 0.99 |
| J. Makazaga | 2 | 11 | 2.53 |
| A. Murua | 3 | 110 | 25.21 |