Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations (Q617033)
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scientific article; zbMATH DE number 5839414
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations |
scientific article; zbMATH DE number 5839414 |
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Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations (English)
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20 January 2011
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A formula for integrals (primitives) of Bernstein polynomials in terms of sums of Bernstein polynomials is given. For a very special class of \(2m\)th 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.
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\(2m\)th order ordinary differential equations
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Galerkin method
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spectral method
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integrals of Bernstein polynomials
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numerical examples
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