Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Rosenbrock methods for partial differential equations and fractional orders of convergence
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Difference Approximations for the Second Order Wave Equation
SIAM Journal on Numerical Analysis
Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems
Applied Numerical Mathematics
Optimal orders of convergence for Runge-Kutta methods and linear, initial boundary value problems
Applied Numerical Mathematics
Applied Numerical Mathematics
Stability of Runge-Kutta-Nyström methods
Journal of Computational and Applied Mathematics
Stability and convergence of staggered Runge-Kutta schemes for semilinear wave equations
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
In this paper, we study the order reduction which turns up when explicit Runge-Kutta-Nystrom methods are used to discretize linear second order hyperbolic equations by means of the method of lines. The order observed in practice, including its fractional part, is obtained. It is also proved that the order reduction can be completely avoided taking the boundary values of the intermediate stages of the time semidiscretization. The numerical experiments confirm that the optimal order can be reached.