euler_heun: Euler-Heun ODE Solver

In pracma: Practical Numerical Math Functions

Euler-Heun ODE Solver

Description

Euler and Euler-Heun ODE solver.

Usage

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)
## Not run: 
plot(s1$t, s1$y, type="l", col="blue")
lines(s2$t, s2$y, col="red")
grid()
## End(Not run)

pracma documentation built on Nov. 10, 2023, 1:14 a.m.