|Lazy evaluation allows for the solution
of differential equations in terms of power series.
Whenever you can express the highest derivative of the solution
as explicit expression of the lower derivatives
where each coefficient of the solution series
depends only on lower coefficients,
the recursive algorithm will work.
Example for a linear equation:
Setup a differential equation for y with
y t = (exp (-t)) * (sin t)
y' t = -(exp (-t)) * (sin t) + (exp (-t)) * (cos t)
y'' t = -2 * (exp (-t)) * (cos t)
Thus the differential equation
y'' = -2 * (y' + y)
The following function generates
a power series for exp (-t) * sin t
by solving the differential equation.
|We are not restricted to linear equations!
Let the solution be y with
y t = (1-t)^-1
y' t = (1-t)^-2
y'' t = 2*(1-t)^-3
then it holds
y'' = 2 * y' * y
|verifyDiffEq1 :: (C a, C a) => [a]||Source|
|Produced by Haddock version 2.4.2|