ivp {cmna}

Initial value problems

Description

solve initial value problems for ordinary differential equations

Usage

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

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)