Adams-Bashford-Moulton
Third-order Adams-Bashford-Moulton predictor-corrector method.
abm3pc(f, a, b, y0, n = 50, ...)
f |
function in the differential equation y' = f(x, y). |
a, b |
endpoints of the interval. |
y0 |
starting values at point |
n |
the number of steps from |
... |
additional parameters to be passed to the function. |
Combined Adams-Bashford and Adams-Moulton (or: multi-step) method of third order with corrections according to the predictor-corrector approach.
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.
This function serves demonstration purposes only.
Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.
## 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) ## Not run: plot(abm1$x, abm1$y, type = "l", col = "blue") lines(abm2$x, abm2$y, type = "l", col = "red") grid() ## End(Not run)
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