Initial value problems

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Description

solve initial value problems for ordinary differential equations

Usage

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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

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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)

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