R: Adams-Bashford-Moulton

abm3pc {pracma} | R Documentation

## 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.

### 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.

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

[Package pracma version 2.0.4 Index]