Integro-differential equation

Integro-differential equation

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 + 5int_{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.

See also

References

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