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Inspired by the Galerkin and particular method, a new approximation approachis recalled in the Cartesian case. In this paper, we are interested speciallyby constructing this method, when the domain of consideration is a twodimensional ball, to extend this work to the several dimension. We reduce thenumber of iterations to calculate integrals and numerical solution of Poissonand the Heat problems (elliptic nd parabolic PDEs), in a very fast way.

Extension of $\delta_{-}ziti$ method in the unit ball: Numerical integration, resolution of Poisson's problem and Heat transfer