Math.Integrators.Implicit

Helpers for implicit integration methods

TODO: add possibility to make function to create initial value TODO: add possibility to break on step TODO: add possibility to add different initial value based on y0, f TODO: add seq-pseq to make this stuff strict TODO: add Newton iterations

types

type ImplicitSolver a

Arguments

 = (a -> a)

implicit method

-> (Int -> a -> a -> Bool)

breakRule

-> a

initial value

-> a

final value

Implicit solver type

solvers

fixedPointSolver :: ImplicitSolver a

Fixed point method it iterates function f until it will break "" will be reached then it returns one but last iteration

fixedPoint

Arguments

:: (a -> a)

function

-> (a -> a -> Bool)

break rule

-> a

initial value

-> a

result

helpers

breakNormR :: Double -> Double -> Bool

simple break rule that will break evaluatioin when value less then Eps

breakNormIR :: (Metric f, Floating a, Ord a, Num (f a)) => f a -> a -> Bool

same as breakNormR but assume that inner type is an instance of InnerField, so it's possible to use innerproduct to find norm N.B function uses $||v||^2 < eps$, so epsilon should be pre evaluated