Arbitrarily high-order energy-conserving methods for Poisson problems

Abstract

In this paper we are concerned with energy-conserving methods for Poisson problems, which are effectively solved by defining a suitable generalization of HBVMs, a class of energy-conserving methods for Hamiltonian problems. The actual implementation of the methods is fully discussed, with a particular emphasis on the conservation of Casimirs. Some numerical tests are reported, in order to assess the theoretical findings.

arXiv comment30 pages, 5 figures, 3 tables

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Cited by in corpus (7)

• (Spectral) Chebyshev collocation methods for solving differential equations
• A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials
• Numerical solution of FDE-IVPs by using Fractional HBVMs: the fhbvm code
• Solving FDE-IVPs by using Fractional HBVMs: some experiments with the fhbvm code
• Continuous-Stage Runge-Kutta approximation to Differential Problems
• A shooting-Newton procedure for solving fractional terminal value problems
• Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function