## An algorithm for solving a nonlinear integro-differential equation.(English)Zbl 1023.65152

Summary: An algorithm based on Adomian’s decomposition method is developed to approximate the solution of the nonlinear integro-differential equation $u_t(x,t)= \int^t_0 a(t-\tau) {\partial\over \partial x} \sigma\bigl(u_x (x,\tau)\bigr) d\tau+ f(x,t),\;0<x<1,\;0<t<T,$
$u(x,0)= \psi(x).$ Special cases of the integro-differential equation are solved using the algorithm. It turns out that the convergence of this algorithm is rapid.

### MSC:

 65R20 Numerical methods for integral equations 45G10 Other nonlinear integral equations 45K05 Integro-partial differential equations
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### References:

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