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.

Solving Ordinary Differential Equations

Zeros of orthogonal polynomials

Orthogonal approximations in Sobolev spaces stability and convergence spectral methods and pseudospectral methods spectral methods for multi-dimensional and high order problems mixed spectral methods combined spectral methods spectral methods on the spherical surface.

Spectral Methods and Their Applications

Simulating Hamiltonian Dynamics: Hamiltonian PDEs

In the article, we establish several new inequalities for the generalized trigonometric and hyperbolic functions with one parameter, generalize the well known Mitrinović-Adamović, Lazarević, Huygens-type, Wilker-type and Cusa-Huygens-type inequalities to the cases of the generalized trigonometric and hyperbolic functions with one parameter.

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Inequalities for generalized trigonometric and hyperbolic functions with one parameter

Time finite element methods: A unified framework for numerical discretizations of ODEs

Construction of Runge-Kutta type methods for solving ordinary differential equations

Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods

Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

On the basis of the previous work by Tang \& Zhang (Appl. Math. Comput. 323, 2018, p. 204--219), in this paper we present a more effective way to construct high-order symplectic integrators for solving second order Hamiltonian equations. Instead of analyzing order conditions step by step as shown in the previous work, the new technique of this paper is using Legendre expansions to deal with the simplifying assumptions for order conditions. With the new technique, high-order symplectic integrators can be conveniently devised by truncating an orthogonal series.

Wensheng Tang

Papers

Time finite element methods: A unified framework for numerical discretizations of ODEs

Construction of Runge-Kutta type methods for solving ordinary differential equations

Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods

Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

High order symplectic integrators based on continuous-stage Runge-Kutta Nystrom methods