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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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