numeric-tools-0.2.0.1: Collection of numerical tools for integration, differentiation etc.

Portability portable experimental Aleksey Khudyakov None

Numeric.Tools.Equation

Contents

Description

Numerical solution of ordinary equations.

Synopsis

# Data type

data Root a Source

The result of searching for a root of a mathematical function.

Constructors

 NotBracketed The function does not have opposite signs when evaluated at the lower and upper bounds of the search. SearchFailed The search failed to converge to within the given error tolerance after the given number of iterations. Root a A root was successfully found.

Instances

 Monad Root Functor Root Typeable1 Root MonadPlus Root Applicative Root Alternative Root Eq a => Eq (Root a) Read a => Read (Root a) Show a => Show (Root a)

Arguments

 :: a Default value. -> Root a Result of search for a root. -> a

Returns either the result of a search for a root, or the default value if the search failed.

# Equations solversv

Arguments

 :: Double Required absolute precision -> (Double, Double) Range -> (Double -> Double) Equation -> Root Double

Use bisection method to compute root of function.

The function must have opposite signs when evaluated at the lower and upper bounds of the search (i.e. the root must be bracketed).

Arguments

 :: Double Absolute error tolerance. -> (Double, Double) Lower and upper bounds for the search. -> (Double -> Double) Function to find the roots of. -> Root Double

Use the method of Ridders to compute a root of a function.

The function must have opposite signs when evaluated at the lower and upper bounds of the search (i.e. the root must be bracketed).

Arguments

 :: Double Absolute error tolerance -> (Double, Double) Lower and upper bounds for root -> (Double -> Double) Function -> (Double -> Double) Function's derivative -> Root Double

Solve equation using Newton-Raphson method. Root must be bracketed. If Newton's step jumps outside of bracket or do not converge sufficiently fast function reverts to bisection.

# References

• Ridders, C.F.J. (1979) A new algorithm for computing a single root of a real continuous function. IEEE Transactions on Circuits and Systems 26:979–980.