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.


65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
45K05 Integro-partial differential equations
Full Text: DOI


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