Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods
Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods
Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
SIAM Journal on Numerical Analysis
Vienna contributions to the development of RK-methods
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Structure Preservation for Constrained Dynamics with Super Partitioned Additive Runge--Kutta Methods
SIAM Journal on Scientific Computing
Nonholonomic motion of rigid mechanical systems from a DAE viewpoint
Nonholonomic motion of rigid mechanical systems from a DAE viewpoint
Numerical methods for ordinary differential equations in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
Exponential Runge-Kutta methods for parabolic problems
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Variational collision integrator for polymer chains
Journal of Computational Physics
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There are two parts in this paper. In the first part we consider an overdetermined system of differential-algebraic equations (DAEs). We are particularly concerned with Hamiltonian and Lagrangian systems with holonomic constraints. The main motivation is in finding methods based on Gauss coefficients, preserving not only the constraints, symmetry, symplecticness, and variational nature of trajectories of holonomically constrained Hamiltonian and Lagrangian systems, but also having optimal order of convergence. The new class of (s,s)-Gauss-Lobatto specialized partitioned additive Runge-Kutta (SPARK) methods uses greatly the structure of the DAEs and possesses all desired properties. In the second part we propose a unified approach for the solution of ordinary differential equations (ODEs) mixing analytical solutions and numerical approximations. The basic idea is to consider local models which can be solved efficiently, for example analytically, and to incorporate their solution into a global procedure based on standard numerical integration methods for the correction. In order to preserve also symmetry we define the new class of symmetrized Runge-Kutta methods with local model (SRKLM).