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In this paper, we use firstly the Laplace-Adomian method to construct the solution of a kind of Fischer's equation and secondly the SBA method to construct the solution of an integral-differential equation.

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This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow -up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.