Duhammel's principle

In mathematics, and more specifically in partial differential equations, Duhamel's principle is the solution to the nonhomogenous wave equation

$u_{tt}-c^2u_{xx}=f(x,t)\,$

with initial conditions

$u(x,0)=u_t(x,0)=0\,$ .

The solution is

$u(x,t) = \frac{1}{2c}\int_0^t\int_{x-c(t-s)}^{x+c(t-s)} f(\xi,s)\,d\xi\,ds\,$

External links

An example of solving a nonhomogenous wave equation from www.exampleproblems.com