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Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations. (English) Zbl 1236.65091
A formula for integrals (primitives) of Bernstein polynomials in terms of sums of Bernstein polynomials is given. For a very special class of 2mth order linear ordinary differential equations, subject to Dirichlet boundary conditions, a numerical approximation method is proposed by integrating the differential equation 2m-times and using Bernstein polynomials as basis functions for a Galerkin method. The above-mentioned formula for integrals of Bernstein polynomials is used to calculate the corresponding matrix elements. Some numerical examples illustrate the approach.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65D30Numerical integration
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