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In this article, a formulation of a point-collocation method in which theunknown function is approximated using global expansion in tensor productBernstein polynomial basis is presented. Bernstein polynomials used in thisstudy are defined over general interval [a,b]. Method incorporates severalideas that enable higher numerical efficiency compared to Bernstein polynomialmethods that have been previously presented. The approach is illustrated by asolution of Poisson, Helmholtz and Biharmonic equations with Dirichlet andNeumann type boundary conditions. Comparisons with analytical solutions aregiven to demonstrate the accuracy and convergence properties of the currentprocedure. The method is implemented in an open-source code, and a library formanipulation of Bernstein polynomials bernstein-poly, developed by the authors.

A Bernstein Polynomial Collocation Method for the Solution of Elliptic Boundary Value Problems