ivp: Initial value problems In cmna: Computational Methods for Numerical Analysis

Description

solve initial value problems for ordinary differential equations

Usage

 ```1 2 3 4 5 6 7``` ```euler(f, x0, y0, h, n) midptivp(f, x0, y0, h, n) rungekutta4(f, x0, y0, h, n) adamsbashforth(f, x0, y0, h, n) ```

Arguments

 `f` function to integrate `x0` the initial value of x `y0` the initial value of y `h` selected step size `n` the number of steps

Details

The `euler` method implements the Euler method for solving differential equations. The codemidptivp method solves initial value problems using the second-order Runge-Kutta method. The `rungekutta4` method is the fourth-order Runge-Kutta method.

Value

a data frame of `x` and `y` values

Examples

 ```1 2 3 4``` ```f <- function(x, y) { y / (2 * x + 1) } ivp.euler <- euler(f, 0, 1, 1/100, 100) ivp.midpt <- midptivp(f, 0, 1, 1/100, 100) ivp.rk4 <- rungekutta4(f, 0, 1, 1/100, 100) ```

cmna documentation built on June 20, 2017, 9:08 a.m.