Euler-Heun ODE Solver

Euler and Euler-Heun ODE solver.

euler_heun(f, a, b, y0, n = 100, improved = TRUE, ...)

Arguments

f

function in the differential equation \(y' = f(x, y)\).

a, b

start and end points of the interval.

y0

starting value at a.

n

number of grid points.

improved

logical; shall the Heun method be used; default TRUE.

...

additional parameters to be passed to the function.

Details

euler_heun is an integration method for ordinary differential equations using the simple Euler resp. the improved Euler-Heun Method.

Value

List with components t for grid (or `time') points, and y the vector of predicted values at those grid points.

References

Quarteroni, A., and F. Saleri (). Scientific Computing with MATLAB and Octave. Second Edition, Springer-Verlag, Berlin Heidelberg, 2006.

See also

cranknic

Examples

##  Flame-up process
f <- function(x, y) y^2 - y^3
s1 <- cranknic(f, 0, 200, 0.01)
s2 <- euler_heun(f, 0, 200, 0.01)
if (FALSE) { # \dontrun{
plot(s1$t, s1$y, type="l", col="blue")
lines(s2$t, s2$y, col="red")
grid()} # }