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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | )abbrev category ODECAT OrdinaryDifferentialEquationsSolverCategory
++ Author: Brian Dupee
++ Date Created: February 1995
++ Date Last Updated: June 1995
++ Description:
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} is the
++ \axiom{category} for describing the set of ODE solver \axiom{domains}
++ with \axiomFun{measure} and \axiomFun{ODEsolve}.
OrdinaryDifferentialEquationsSolverCategory() : Category == SIG where
DFF ==> DoubleFloat
VEDFF ==> Vector Expression DoubleFloat
LDFF ==> List DoubleFloat
EDFF ==> Expression DoubleFloat
ODEAF ==> Record(xinit:DFF,xend:DFF,fn:VEDFF,yinit:LDFF,intvals:LDFF,
g:EDFF,abserr:DFF,relerr:DFF)
SIG ==> SetCategory with
measure : (RoutinesTable,ODEAF) ->
Record(measure:Float,explanations:String)
++ measure(R,args) calculates an estimate of the ability of a particular
++ method to solve a problem.
++
++ This method may be either a specific NAG routine or a strategy (such
++ as transforming the function from one which is difficult to one which
++ is easier to solve).
++
++ It will call whichever agents are needed to perform analysis on the
++ problem in order to calculate the measure. There is a parameter,
++ labelled \axiom{sofar}, which would contain the best compatibility
++ found so far.
ODESolve : ODEAF -> Result
++ ODESolve(args) performs the integration of the
++ function given the strategy or method returned by \axiomFun{measure}.
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