Solutions of 2nd-order linear differential equations subject to Dirichlet boundary conditions in a Bernstein polynomial basis (Q458916)

This paper deals with an algorithm based on a Bernstein polynomial basis and its dual for solving second-order linear differential equations subject to Dirichlet conditions by approximating the solution in the \(B\)-polynomials. The procedure takes advantage of the continuity and unity partition properties of the basis set of \(B\)-polynomials over the interval \([0,1]\). Some examples with constant and polynomial coefficients are presented. Also, an approach for solving a second-order parabolic linear differential equation subject to initial-boundary conditions is outlined.