solve initial value problems for ordinary differential equations
euler(f, x0, y0, h, n)
midptivp(f, x0, y0, h, n)
rungekutta4(f, x0, y0, h, n)
adamsbashforth(f, x0, y0, h, n)| 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 |
a data frame of x and y values
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.
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)