pracma (version 1.2.0)

abm3pc: Adams-Bashford-Moulton

Description

Third-order Adams-Bashford-Moulton predictor-corrector method.

Usage

abm3pc(f, a, b, y0, n = 50, ...)

Arguments

f

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

a, b

endpoints of the interval.

y0

starting values at point a.

n

the number of steps from a to b.

...

additional parameters to be passed to the function.

Value

• List with components x for grid points between a and b and y a vector y the same length as x; additionally an error estimation est.error that should be looked at with caution.

Details

Combined Adams-Bashford and Adams-Moulton (or: multi-step) method of third order with corrections according to the predictor-corrector approach.

References

Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.

See Also

rk4, ode23

Examples

##  Attempt on a non-stiff equation
#   y' = y^2 - y^3, y(0) = d, 0 <= t <= 2/d, d = 0.01
f <- function(t, y) y^2 - y^3
d <- 1/250
abm1 <- abm3pc(f, 0, 2/d, d, n = 1/d)
abm2 <- abm3pc(f, 0, 2/d, d, n = 2/d)
plot(abm1$x, abm1$y, type = "l", col = "blue")
lines(abm2$x, abm2$y, type = "l", col = "red")
grid()