# A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations

@article{Byrne1975APF, title={A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations}, author={George D. Byrne and Alan C. Hindmarsh}, journal={ACM Trans. Math. Softw.}, year={1975}, volume={1}, pages={71-96} }

Two variable-order, varlable-step size methods for the numerical solution of the initial value problem for ordinary differential equations are presented. These methods share a common philosophy and have been combined in a single program. The two integrators are for stiff and nonstiff ordinary differential equations, respectively. The former integrator is based on backward differentiation formulas of orders one through five, each of which is stiffly stable, while the latter is based on formulas…

## 266 Citations

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