Journal of Computational and Applied Mathematics
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Symbolic derivation of Runge-Kutta methods
Journal of Symbolic Computation
A new recurrence for computing Runge-Kutta truncation error coefficients
SIAM Journal on Numerical Analysis
A general family of explicit Runge-Kutta pairs of orders 6(5)
SIAM Journal on Numerical Analysis
Cheap Error Estimation for Runge--Kutta Methods
SIAM Journal on Scientific Computing
High Phase-Lag-Order Runge--Kutta and Nyström Pairs
SIAM Journal on Scientific Computing
Optimized explicit Runge-Kutta pair of orders 9(8)
Applied Numerical Mathematics
The Mathematica Book
Canonical integration methods for Hamiltonian dynamical systems
Canonical integration methods for Hamiltonian dynamical systems
ACM Transactions on Mathematical Software (TOMS)
Stage reduction on P-stable numerov type methods of eighth order
Journal of Computational and Applied Mathematics - Special issue: The international conference on computational methods in sciences and engineering 2004
Symbolic derivation of Runge-Kutta order conditions
Journal of Symbolic Computation
| Hi-index | 7.29 |
Numerov-type ODE solvers are widely used for the numerical treatment of second-order initial value problems. In this work we present a powerful and efficient symbolic code in MATHEMATICA for the derivation of their order conditions and principal truncation error terms. The relative tree theory for such order conditions is presented along with the elements of combinatorial mathematics, partitions of integer numbers and computer algebra which are the basis of the implementation of the symbolic code.