Regular order reductions of ordinary and delay-differential equations. J.M. Aguirregabiria, Ll. Bel, A. Hernandez, M. Rivas.

PROGRAM SUMMARY
Title of program: ODEred
Catalogue identifier: ADJT
Ref. in CPC: 116(1999)95
Operating system: Windows 95, Digital Unix v.4.08, Open VMS V6.1
High speed store required: 1MK words
Number of lines in distributed program, including test data, etc: 3262
Programming language used: C
Computer: PC

Nature of physical 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.

Method of solution
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.

Typical 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.