desolve_rk4( equation, variable, ics=[initial_conditions] [ , options ] )

The numerical solution in SageMath of the first-order differential equation for dependent variable. The argument equation can be either the right-hand side of an equation or a complete symbolic equation. The dependent variable must be declared as a function of the independent variable for a symbolic equation.

Equations in SageMath need to be defined with double equal (==) signs to avoid syntax errors.

Initial conditions are given for the independent variable and the dependent variable, in that order.

Available options are:

ivar=independent_variable
end_points=value|[values]
step=value
output='list'|'plot'|'slope_field'

The independent variable must be specified if the equation contains more than one independent variable or if the independent variable does not appear explicitly.

Examples:

y = function('y')(x)
desolve_rk4( diff(y,x) == x, y, ics=[0,1] )

var('y')
desolve_rk4( x, y, ics=[0,1] )

var('y')
desolve_rk4( x, y, ics=[0,1], output='plot' )

Related operations:   desolve

Operation category: solution operations sagemath-docs