THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING
LAPLACIAN PRESERVING TRANSFORMATION OF SURFACES AND APPLICATION TO BOUNDARY VALUE PROBLEMS FOR LAPLACE’S AND POISSON’S EQUATIONS
This paper shows that the constrained similarity transformation of surfaces under boundary constraints is a Laplacian preserving transformation. First, a general proof is presented and then the result is verified for mesh-functions through particular examples. The fact that the constrained similarity transformation, subject to boundary constraints, is a Laplacian preserving transformation is used to construct a method for solving boundary value problems for the Laplace’s and the Poisson’s equations. Given any solution to these equations we apply the constrained similarity transformation to get the particular solution that satisfies the given boundary conditions.