R: Solution of Autonomous Linear Differential Equations

lin.diff.eqn {rmutil} | R Documentation

## Solution of Autonomous Linear Differential Equations

### Description

`lin.diff.eqn` numerically solves a system of autonomous linear differential equations with given initial conditions by matrix exponentiation.

### Usage

    lin.diff.eqn(A, initial, t=1)

### Arguments

`A` | A square matrix giving the coefficients of the equations.
`initial` | The vector of initial values of the system.
`t` | A scalar or vector of values of the independent variable for which solutions are sought.

### Value

A matrix of solutions with one row for each value of `t`.

### Author(s)

J.K. Lindsey

### Examples

    a <- matrix(c(1,0,1,0,0,0,0,0,-1),ncol=3,byrow=TRUE)
    x <- c(5,7,6)
    lin.diff.eqn(a,x,1)
    # function giving the exact solution
    exact <- function(t) c(8*exp(t)-3*exp(-t),7,6*exp(-t))
    exact(1)

[Package rmutil version 1.1.3 Index]