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

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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

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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)

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