As it is well known in numerical analysis, most of the numerical schemes have undesirable oscillations, especially near the domain's border, or near the physical phenomena (empty region, collapse, boundary layer, among others)(mathematically invisible) eg: the heat equation with a bad sign, Burgers equation(the solution loses its regularity).\\ In the case where the differential problem solution presents a singularity (shock, blow-up which cannot be numerically detected easily), the classical scheme cannot generally operate correctly and in the best case we are confronted with a very difficult algorithm, especially in several dimensions. \\ Our objective here is to construct a less complicated scheme compared to the classical methods by keeping their advantages and obtained the admissible solution in the most difficult situations without complications obtained from the selected meshing.\\ In this paper, we present a new method called ziti's $\delta$- scheme which is able to resist to such oscillation near the singularity and enables us to detect a lot of physical phenomena. In particular, with our method, we construct a multidimensional numerical integration and compare its results with other methods. \\ We depict the ziti's $\delta$- scheme for the multidimensional partial differential equations and systems on any meshing with simple numbering. We apply our method to some models and compare its results with the exact one and other classical numerical methods.\\ We can conclude that our results are very striking. The ziti's $\delta$- method that we obtained is faster and more efficient and robust.\\

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