manifolds-0.6.1.0: Coordinate-free hypersurfaces
Copyright(c) Justus Sagemüller 2016
LicenseGPL v3
Maintainer(@) jsag $ hvl.no
Stabilityexperimental
Portabilityportable
Safe HaskellSafe-Inferred
LanguageHaskell2010

Data.Manifold.DifferentialEquation

Description

 
Synopsis

Formulating simple differential eqns.

type DifferentialEqn ㄇ x y = Shade (x, y) -> LocalDifferentialEqn ㄇ x y Source #

type ODE x y = DifferentialEqn QuadraticModel x y Source #

An ordinary differential equation is one that does not need any a-priori partial derivatives to compute the derivative for integration in some propagation direction. Classically, ODEs are usually understood as DifferentialEquation ℝ ℝ⁰ y, but actually x can at least be an arbitrary one-dimensional space (i.e. basically real intervals or ). In these cases, there is always only one partial derivative: that which we integrate over, in the only possible direction for propagation.

constLinearDEqn :: forall x y. (SimpleSpace x, SimpleSpace y, AffineManifold y, Scalar x ~ , Scalar y ~ ) => (y +> (x +> y)) -> ((x +> y) +> y) -> DifferentialEqn QuadraticModel x y Source #

constLinearODE :: forall x y. (SimpleSpace x, Scalar x ~ , AffineManifold y, SimpleSpace y, Scalar y ~ ) => ((x +> y) +> y) -> ODE x y Source #

iterateFilterDEqn_static :: (ModellableRelation x y, MonadPlus m, LocalModel ㄇ) => InformationMergeStrategy [] m (x, Shade' y) iy -> Embedding (->) (Shade' y) iy -> DifferentialEqn ㄇ x y -> PointsWeb x (Shade' y) -> Cofree m (PointsWeb x (Shade' y)) Source #

Cost functions for error bounds

Solver configuration