Duhamel's principle

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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\,

[edit] External links

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