Module mathru::analysis::differential_equation::ordinary

Ordinary differential equation

Fore more information:
https://en.wikipedia.org/wiki/Ordinary_differential_equation Because ODE higher order can always be reduced to a system of first order ODEs, the implemented algorithms only support to solve first order ODEs.

\frac{dy}{dt}=f(t, y)

Modules

problem

Structs

AdamsBashforth	Adams-Bashforth method
BDF	Backward differentitation formula
BogackiShampine32	Solves an ODE using the Bogacki Shampine algorithm.
CashKarp54	Solves an ODE using the 4th order Cash-Karp algorithm.
DormandPrince54	Solves an ODE using the 5th order Runge-Kutta-Dormand-Prince algorithm.
ExplicitEuler	Solves an ODE using Euler's method.
Heun	Solves an ODE using Heun's method.
ImplicitEuler	Solves an ODE using backward Euler
Kutta3	Solves an ODE using the 3th order Runge-Kutta algorithm.
Midpoint	Solves an ODE using midpoint method.
Ralston	Solves an ODE using Ralston's method.
RungeKutta4	Solves an ODE using the 4th order Runge-Kutta algorithm.
RungeKuttaFehlberg54	Solves an ODE using the 4th order Runge-Kutta-Fehlberg algorithm.

Traits

ExplicitODE	Explicit ODE algrithm interface
ImplicitODE	Implicit ordinary differential equation