A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di
erential equations (ODEs) is undertaken. The goal of this review is to summarize the …

A general analysis of accuracy and linear stability of Runge–Kutta–Nyström (RKN) methods
for solving second-order stiff problems is carried out. This analysis reveals that when …

This paper discusses a new class of optimized implicit-explicit Runge-Kutta methods for the
numerical solution of the dispersive and non-dispersive hyperbolic systems. Optimized …

This article presents constrained numerical optimization of high-order linearly and
algebraically stable diagonally-implicit Runge–Kutta methods. After satisfying the desired …

Visually appealing and vivid simulations of deformable solids represent an important aspect
of physically based computer animation. For the temporal discretization, it is customary in …

New SDIRKN methods specially adapted to the numerical integration of second-order stiff
ODE systems with periodic solutions are obtained. Our interest is focused on the dispersion …

New symmetric DIRK methods specially adapted to the numerical integration of first-order
stiff ODE systems with periodic solutions are obtained. Our interest is focused on the …

The numerical integration of Hamiltonian systems is considered in this paper. Diagonally
implicit Symplectic Runge-Kutta methods with special properties are presented. The …

This paper is concerned with the numerical approximation of initial‐boundary‐value
problems of a three‐parameter family of Bona–Smith systems, derived as a model for the …

Nonlinear diffusion equations are extensively applicable in diverse fields of science and
engineering. Numerical stability is a common concern in this class of equations. In the …