An extended framework of continuous-stage Runge-Kutta methods

Abstract

We propose an extended framework for continuous-stage Runge-Kutta methods which enables us to treat more complicated cases especially for the case weighting on infinite intervals. By doing this, various types of weighted orthogonal polynomials (e.g., Jacobi polynomials, Laguerre polynomials, Hermite polynomials etc.) can be used in the construction of Runge-Kutta-type methods. Particularly, families of Runge-Kutta-type methods with geometric properties can be constructed in this new framework. As examples, some new symplectic integrators by using Legendre polynomials, Laguerre polynomials and Hermite polynomials are constructed.

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References in corpus (4)

• Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
• A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems
• Continuous-stage Runge-Kutta methods based on weighted orthogonal polynomials
• Chebyshev symplectic methods based on continuous-stage Runge-Kutta methods

Cited by in corpus (5)

• Continuous-stage Runge-Kutta-NystrÖm methods
• Energy-preserving continuous-stage partitioned Runge-Kutta methods
• Symmetric integrators based on continuous-stage Runge-Kutta-Nystrom methods for reversible systems
• Energy-preserving continuous-stage Runge-Kutta-Nyström methods
• Energy-preserving integration of non-canonical Hamiltonian systems by continuous-stage methods