Integro-differential equation

From Wikipedia, the free encyclopedia

An integro-differential equation is an equation which has both integrals and derivatives of an unknown function. The equation is of the form

\frac{dx(t)}{dt} = f(t,x(t))+ \int_{t_0}^t K(t,s,x(s))\,ds

where

x(t_0) = x_0, t_0 \ge 0

For example:

\frac{di}{dt} + 2i + 5\int_{0}^{t}i\,dt = u(t),\quad i(0)=0.

An integro-differential equation is similar to a differential equation; therefore, tools such as the Laplace transform can be used to solve the equation.

[edit] Also See

[edit] References

  • [1] at Interactive Mathematics
  • Vangipuram Lakshmikantham, M. Rama Mohana Rao, ``Theory of Integro-Differential Equations,CRC Press, 1995