# abm3: Adams-Bashford-Moulton In pracma: Practical Numerical Math Functions

 abm3pc R Documentation

### 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.

### Details

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

### 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.

### Note

This function serves demonstration purposes only.

### References

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

`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)
## Not run:
plot(abm1\$x, abm1\$y, type = "l", col = "blue")
lines(abm2\$x, abm2\$y, type = "l", col = "red")
grid()
## End(Not run)
``````

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