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Class jDisco.Implicit

java.lang.Object
   |
   +----jDisco.Implicit

public abstract class Implicit
extends java.lang.Object
In describing continuous processes it is the user's responsibility that the equations are evaluated in the correct order: variables must be updated before they are used on the right-hand side of an equation.

The user can determine the order of evaluation within each continuous process and the continuous processes themselves may be ranked by giving them a priority. Usually by these means a correct evaluation order can be achieved.

In some cases, however, this is impossible: there is an "algebraic loop" in the equation system.

An algebraic loop can often be circumvented by either rewriting the equations or using the class Implicit.

Class Implicit is used to solve equations of the form

         x = f(x) 
that is, to find the fixpoint of the function f.

The mthod fixPoint finds an x satsifying the equation with a given tolerance, tol, i.e.

        |x - f(x)| <= |tol| 
Wegstein's accelerated convergence algorithm is used to compute x. The algorithm is iterative and uses the paramter value of x as an initial guess for x.

If the tolerance criterion is not satisfied after 100 iterations, the program stops with the error message:


         Implicit: Convergence is not achieved within 100 iterations 
 


Constructor Index

 o Implicit()

Method Index

 o f(double)
The function f.
 o fixPoint()
Returns the fixpoint of the function f with 1 as an initial guess for x and tolerance of 1.0e-5.
 o fixPoint(double, double)
Returns the fixpoint of the function f.

Constructors

 o Implicit
 public Implicit()

Methods

 o f
 protected abstract double f(double x)
The function f. To be supplied in a subclass of Implicit.

 o fixPoint
 public double fixPoint(double x,
                        double tol)
Returns the fixpoint of the function f.

Parameters:
x - initial guess for x.
tol - the tolerance.
 o fixPoint
 public double fixPoint()
Returns the fixpoint of the function f with 1 as an initial guess for x and tolerance of 1.0e-5.


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