Author
G. R. W. Quispel
Other affiliations: Clarkson University, Australian National University, Utrecht University ...read more
Bio: G. R. W. Quispel is an academic researcher from La Trobe University. The author has contributed to research in topics: Integrable system & Differential equation. The author has an hindex of 38, co-authored 167 publications receiving 6422 citations. Previous affiliations of G. R. W. Quispel include Clarkson University & Australian National University.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the conformal anomaly and surface exponents of the critical quantum Ashkin-Teller and Potts chains are calculated by exploiting their relations with the mass gap amplitudes as predicted by conformal invariance.
Abstract: Eigenspectra of the critical quantum Ashkin-Teller and Potts chains with free boundaries can be obtained from that of the XXZ chain with free boundaries and a complex surface field. By deriving and solving numerically the Bethe ansatz equations for such boundaries the authors obtain eigenenergies of XXZ chains of up to 512 sites. The conformal anomaly and surface exponents of the quantum XXZ, Ashkin-Teller, and Potts chains are calculated by exploiting their relations with the mass gap amplitudes as predicted by conformal invariance.
496 citations
15 Apr 1999-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: The discrete analogue of the gradient of a function is discussed and how discrete gradients can be used in the numerical integration of ordinary differential equations (ODEs) is shown.
Abstract: This paper discusses the discrete analogue of the gradient of a function and shows how discrete gradients can be used in the numerical integration of ordinary differential equations (ODEs). Given a...
492 citations
TL;DR: In this article, it was shown that simple solutions of discrete soliton equations satisfy 2D mappings and that these belong to a recently introduced 18-parameter family of integrable reversible mappings of the plane.
408 citations
TL;DR: The first energy-preserving B-series numerical integration method for (ordinary) differential equations is presented and applied to several Hamiltonian systems in this article, where the first ever energy preserving B series numerical integration algorithm is presented.
Abstract: The first ever energy-preserving B-series numerical integration method for (ordinary) differential equations is presented and applied to several Hamiltonian systems. Related novel Lie algebraic results are also discussed.
403 citations
TL;DR: In this paper, an 18-parameter family of integrable reversible mappings of the plane is presented, which are shown to occur in soliton theory and in statistical mechanics.
311 citations
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01 Mar 1987
TL;DR: The variable-order Adams method (SIVA/DIVA) package as discussed by the authors is a collection of subroutines for solution of non-stiff ODEs.
Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
1,955 citations
TL;DR: In this paper, a new class of boundary conditions for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method is described, which allows the author to treat open quantum chains with appropriate boundary terms in the Hamiltonian.
Abstract: A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open quantum chains with appropriate boundary terms in the Hamiltonian. The general considerations are applied to the XXZ and XYZ models, the nonlinear Schrodinger equation and Toda chain.
1,774 citations
TL;DR: In this paper, a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles is presented, including the Verlet, SHAKE, RATTLE, Newmark, and the symplectic partitioned Runge-Kutta schemes.
Abstract: This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints in a natural way. Amongst the many specific schemes treated as examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplectic partitioned Runge–Kutta schemes are presented.
1,657 citations
TL;DR: Magnusson expansion as discussed by the authors provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory (TEPT).
1,013 citations
TL;DR: In this paper, some new similarity reductions of the Boussinesq equation, which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering, are presented.
Abstract: Some new similarity reductions of the Boussinesq equation, which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering, are presented. These new similarity reductions, including some new reductions to the first, second, and fourth Painleve equations, cannot be obtained using the standard Lie group method for finding group‐invariant solutions of partial differential equations; they are determined using a new and direct method that involves no group theoretical techniques.
922 citations