Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4643040 | Journal of Computational and Applied Mathematics | 2007 | 21 Pages |
Abstract
Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge–Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge–Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Hoang Si Nguyen, Roger B. Sidje, Nguyen Huu Cong,