A rational approximation based on Bernstein polynomials for high order initial and boundary values problems |
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Authors: | Osman Ra?it I?ikMehmet Sezer Zekeriya Güney |
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Institution: | a Department of Mathematics, Faculty of Science, Mu?la University, 48000 Mu?la, Turkey b Department of Mathematics, Faculty of Education, Mu?la University, 48000 Mu?la, Turkey |
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Abstract: | We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann 1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution f ∈ Cd+2a, b]. |
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Keywords: | Rational interpolation Differential equations Approximate solution Collocation method Bernstein polynomials |
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