Function Repository Resource:

# RungeKuttaDSolve

Solve differential equations using one of the Runge–Kutta or related methods

Contributed by: Jason Martinez
 ResourceFunction["RungeKuttaDSolve"][eqns,u,{x,xmin,xmax}, method] finds a numerical solution to the ordinary differential equations eqns for the function u with the independent variable x in the range xmin to xmax using the specified method. ResourceFunction["RungeKuttaDSolve"][eqns,u,{x,xmin,xmax},property,method] returns a specific property for the numerical calculation.

## Details and Options

ResourceFunction["RungeKuttaDSolve"] gives results in terms of InterpolatingFunction objects.
ResourceFunction["RungeKuttaDSolve"] supports most of the functionality and options for NDSolve but inserts the proper method options for the specified method.
method specifications include:
 "DOPRI" Dormand–Prince method "ExplicitEuler" Forward Euler method "ExplicitMidpoint" Explicit midpoint method "Heun" Heun's method "ImplicitEuler" backward Euler method "ImplicitMidpoint" implicit midpoint method "RK3" 3rd order Runge–Kutta method "RK4" 4th order Runge–Kutta method "RKBS" Bogacki–Shampine method "RKF" Runge–Kutta–Fehlberg method
The function u must depend only on the single variable x.
The differential equations must contain enough initial or boundary conditions to determine the solutions for u completely.
property can take any of the following values:
 "Solution" interpolation function for the solution to u "Steps" Stepwise results "ButcherTableau" Butcher tableau for the method
"PropertyAssociation" can be used to return an Association of the properties.

## Examples

### Basic Examples (1)

Solve a differential equation using the fourth order Runge-Kutta method:

 In[1]:=
 Out[1]=

### Scope (3)

Find the Butcher tableau for the Dormand–Prince method:

 In[2]:=
 Out[2]=

Compute the steps to determine the interpolation function:

 In[3]:=
 Out[3]=

Get a property association of all properties:

 In[4]:=
 Out[4]=

## Version History

• 1.0.0 – 08 August 2022