We consider the Weil-Petersson form on the Teichmüller space T (S) of a surface S of genus at least 2, and we compute it in terms of the shearing coordinates for T (S) associated to a geodesic lamination λ on S. In the corresponding expression, the Weil-Petersson form coincides with Thurston's intersection form on the space of transverse cocycles for λ.

A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Dirichlet condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.

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