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Manuscript Title: Regular order reductions of ordinary and delay-differential equations.
Authors: J.M. Aguirregabiria, Ll. Bel, A. Hernandez, M. Rivas
Program title: ODEred
Catalogue identifier: ADJT_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 116(1999)95
Programming language: C.
Computer: PC.
Operating system: Windows 95, Digital Unix v.4.08, Open VMS V6.1.
RAM: 1M words
Keywords: General purpose, Ordinary, Differential equations, Delay-differential, Equations, Order reduction, Lorentz-dirac equation, Abraham-lorentz equation, Chaotic scattering.
Classification: 4.3.

Nature of problem:
In different physical problems, including electrodynamics and theories of gravitation, there appear singular differential equations whose order decreases when a physical parameter takes a particular but very important value. Typically most solutions of these equations are unphysical. The regular order reduction is an equation of lower order which contains precisely the physical solutions, which are those regular in that parmeter. The program computes the solution of the regular order reduction for a large set of ordinary and delay-differential equations.

Solution method:
The basic integration routine is based on the continuous Prince-Dormand method of eight order. At each integration step, successive approximations are performed by using the polynomial interpolating the solution that has been computed in the previous approximation.

Running time:
It depends heavily on the number and complexity of the equations and on the desired solution range. It was at most a couple of seconds in the test problems.