2012/11/15 by Nikola Mirkov, Mirkov, Nikola, Boško Rašuo +1
Engineering · Mathematics · #Computational Physics (physics.comp-ph) #Differential Equations and Boundary Problems #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1211.3567
openalex publication_date 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are defined over general interval [a,b]. Method incorporates several ideas that enable higher numerical efficiency compared to Bernstein polynomial methods that have been previously presented. The approach is illustrated by a solution of Poisson, Helmholtz and Biharmonic equations with Dirichlet and Neumann type boundary conditions. Comparisons with analytical solutions are given to demonstrate the accuracy and convergence properties of the current procedure. The method is implemented in an open-source code, and a library for manipulation of Bernstein polynomials bernstein-poly, developed by the authors.