freegraph
Class EquationSolver

java.lang.Object
  |
  +--freegraph.EquationSolver

public class EquationSolver

extends java.lang.Object

class with static functions to find solutions to equations using either Newton's Method or Bisection techniques.

Constructor Summary

EquationSolver()

Method Summary

static double	bisection(ExpressionEvaluator expr1, ExpressionEvaluator expr2, double low, double high, double tolerance, char solveFor) attempts to solve the equation expr1=exrp2 using bisection looking between low and high
static void	main(java.lang.String[] args)
static double	newton(ExpressionEvaluator expr1, ExpressionEvaluator expr2, double value, double tolerance, double slopeLimit, char solveFor) attempts to zero in on a solution using Newtons equation solving technique.
static double	repeatBisection(ExpressionEvaluator expr1, ExpressionEvaluator expr2, double low, double high, double tolerance, char solveFor) attempts to solve the equation expr1=exrp2 using bisection repeatedly by moving trying various starting points.
static double	repeatNewton(ExpressionEvaluator expr1, ExpressionEvaluator expr2, double value, double tolerance, double slopeLimit, char solveFor) attempts to solve the equation expr1=exrp2 using Newton's method and repeatedly moving to different starting points looking for an answer.
static double	xintercept(ExpressionEvaluator expr1, ExpressionEvaluator expr2, double value, double tolerance, double slopeLimit, char solveFor) returns the X-Intercept of the tangent to the equation expr1=expr2 at value.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

EquationSolver

public EquationSolver()

Method Detail

repeatNewton

public static double repeatNewton(ExpressionEvaluator expr1,
                                  ExpressionEvaluator expr2,
                                  double value,
                                  double tolerance,
                                  double slopeLimit,
                                  char solveFor)
                           throws NoSolutionException

attempts to solve the equation expr1=exrp2 using Newton's method and repeatedly moving to different starting points looking for an answer.

Parameters:

expr1 - the left side of the equation.

expr2 - the rigth side of the equation.

value - the x value.

tolerance - the tolerance of the solution (how close to the actual answer must the result be)

slopeLimit - the difference in x values used in estimating the slope of the line

Returns:

a solution to the equation expr1=expr2.

Throws:

NoSolutionException - if no solution can be found

newton

public static double newton(ExpressionEvaluator expr1,
                            ExpressionEvaluator expr2,
                            double value,
                            double tolerance,
                            double slopeLimit,
                            char solveFor)
                     throws NoSolutionException

attempts to zero in on a solution using Newtons equation solving technique.

Parameters:

expr1 - the left side of the equation.

expr2 - the rigth side of the equation.

value - the x value.

tolerance - the tolerance of the solution (how close to the actual answer must the result be)

slopeLimit - the difference in x values used in estimating the slope of the line

Returns:

a solution to the equation expr1=expr2.

Throws:

NoSolutionException - if no solution can be found

repeatBisection

public static double repeatBisection(ExpressionEvaluator expr1,
                                     ExpressionEvaluator expr2,
                                     double low,
                                     double high,
                                     double tolerance,
                                     char solveFor)
                              throws NoSolutionException

attempts to solve the equation expr1=exrp2 using bisection repeatedly by moving trying various starting points.

Parameters:

expr1 - the left side of the equation.

expr2 - the rigth side of the equation.

low - the low value to start in the bisection

high - the high value to start in the bisection

tolerance - the tolerance of the solution (how close to the actual answer must the result be)

Returns:

a solution to the equation expr1=expr2.

Throws:

NoSolutionException - if no solution can be found

bisection

public static double bisection(ExpressionEvaluator expr1,
                               ExpressionEvaluator expr2,
                               double low,
                               double high,
                               double tolerance,
                               char solveFor)
                        throws NoSolutionException

attempts to solve the equation expr1=exrp2 using bisection looking between low and high

Parameters:

expr1 - the left side of the equation.

expr2 - the rigth side of the equation.

low - the low value to start in the bisection

high - the high value to start in the bisection

tolerance - the tolerance of the solution (how close to the actual answer must the result be)

Returns:

a solution to the equation expr1=expr2.

Throws:

NoSolutionException - if no solution can be found

xintercept

public static double xintercept(ExpressionEvaluator expr1,
                                ExpressionEvaluator expr2,
                                double value,
                                double tolerance,
                                double slopeLimit,
                                char solveFor)
                         throws freegraph.EquationSolver.SolutionFound

returns the X-Intercept of the tangent to the equation expr1=expr2 at value. (This method is used by the Newtonian solving methods)

Parameters:

expr1 - the left side of the equation.

expr2 - the rigth side of the equation.

tolerance - the tolerance of the solution (how close to the actual answer must the result be)

slopeLimit - the difference in x values used in estimating the slope of the line

Returns:

the xintercept

Throws:

SolutionFound - is the xintercept is a solution to the equation expr1=expr2 within tolerance.

freegraph.EquationSolver.SolutionFound

main

public static void main(java.lang.String[] args)