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This article presents for the first time the differential equations of the complete loading characteristics of three phase axial flux permanent magnet synchronous machine (AFPMSM) with broad air-gap. It shows that this characteristic leads to algebraic differential equations (ADE), which we know recently, the properties and integrated numerical means. These equations are governed by a multidistributed value problem (MDVP) which makes this problem a difficult numerical one, non accessible by traditional solvers. This article shows thanks to the properties of Ck spline functions that we can integrated such problems by judicious choices of the initial vectors and simulated annealing methods. The first results of simulations will be given.