Evaluation of a Test Set for Stiff ODE Solvers
ACM Transactions on Mathematical Software (TOMS)
Highly continuous Runge-Kutta interpolants
ACM Transactions on Mathematical Software (TOMS)
Algorithm 694: a collection of test matrices in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
ACM Transactions on Mathematical Software (TOMS)
An MEBDF code for stiff initial value problems
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
A modified Adams method for nonstiff and mildly stiff initial value problems
ACM Transactions on Mathematical Software (TOMS)
Algorithm 648: NSDTST and STDTST: routines for assessing the performance of IV solvers
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
DESI methods for stiff initial-value problems
ACM Transactions on Mathematical Software (TOMS)
A test package for Sturm-Liouville solvers
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Corrigenda: “Two FORTRAN Packages for Assessing Initial Value Methods”
ACM Transactions on Mathematical Software (TOMS)
Corrigenda: “An Efficient Derivative-Free Method for Solving Nonlinear Equations”
ACM Transactions on Mathematical Software (TOMS)
Variable-order starting algorithms for implicit Runge-Kutta methods on stiff problems
Applied Numerical Mathematics
Speeding up Netwton-type iterations for stiff problems
Journal of Computational and Applied Mathematics
N-body simulations: The performance of some integrators
ACM Transactions on Mathematical Software (TOMS)
Robust and reliable defect control for Runge-Kutta methods
ACM Transactions on Mathematical Software (TOMS)
ADIFOR-Generating Derivative Codes from Fortran Programs
Scientific Programming
The NUMOL solution of time-dependent PDEs using DESI Runge-Kutta formulae
Applied Numerical Mathematics
A new embedded pair of Runge-Kutta formulas of orders 5 and 6
Computers & Mathematics with Applications
VSVO formulation of the taylor method for the numerical solution of ODEs
Computers & Mathematics with Applications
Speeding up Newton-type iterations for stiff problems
Journal of Computational and Applied Mathematics
A one-step 7-stage Hermite-Birkhoff-Taylor ODE solver of order 11
Journal of Computational and Applied Mathematics
Runge-Kutta pairs of order 5(4) satisfying only the first column simplifying assumption
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS
ACM Transactions on Mathematical Software (TOMS)
High order explicit Runge---Kutta Nyström pairs
Numerical Algorithms
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We present a discussion and description of a collection of FORTRAN routines designed to aid in the assessment of initial value methods for ordinary differential equations. Although the overall design characteristics are similar to those of earlier testing packages [2,6] that were used for the comparison of methods [5,7], the details and objectives of the current collection are quite different. Our principal objective is the development of testing tools that can be used to assess the efficiency and reliability of a standard numerical method without requiring significant modifications to the method and without the tools themselves affecting the performance of the method.