90 Package rk_adaptive

90.1 Introduction to rk_adaptive

rk_adaptive employs the runge-kutta method for numberically solving differential equations, but other than rk it tries to find a sensible step size, which reduces both runtime and amount of data produced.

90.2 Functions and Variables for rk_adaptive

Function: rk_adaptive (expr, vars, vars_initval, var,

startval, endval, params1...)

Tries to solve the ODE whose derivates are defined by expr to the variables vars, starting at their initial values vars_initval. The independent variable (in physics: normally time) is var, being stepped from startval to endval.

Sometimes it speeds up the calculation to use a floating-point number as startval, as using floars will prevent all results from becoming endless rational numbers.

The following optional parameters are accepted:

• maxstep=num: The maximum step size to be used.
• minstep=num: The minimum step size to be used.
• timestep_initial=num: The initial guess for the optimum time step to start with.
• maxabserr=num: The maximum absolute error of the resulting curves.
• maxrelerr=num: The maximum relative error of the resulting curves as a fallback for variables with big values for which maxabserr might be too sensitive.

See also rk.

Example:

(%i1) pnts:rk_adaptive(-1/10*x,x,1,t,0,100)  $