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

## Description

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

## Usage

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## 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) ```

### Example output

```
```

pracma documentation built on Dec. 11, 2021, 9:57 a.m.