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Solving Nonholonomic Systems with the Tau Method
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Almost Exact Computation of Eigenvalues in Approximate Differential Problems

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Instituto Superior de Engenharia do Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
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Centro de Matemática da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
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Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, s/n, 4169-007 Porto, Portugal
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Math. Comput. Appl. 2019, 24(4), 96; https://doi.org/10.3390/mca24040096
Received: 29 September 2019 / Revised: 12 November 2019 / Accepted: 13 November 2019 / Published: 14 November 2019
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)
Differential eigenvalue problems arise in many fields of Mathematics and Physics, often arriving, as auxiliary problems, when solving partial differential equations. In this work, we present a method for eigenvalues computation following the Tau method philosophy and using Tau Toolbox tools. This Matlab toolbox was recently presented and here we explore its potential use and suitability for this problem. The first step is to translate the eigenvalue differential problem into an algebraic approximated eigenvalues problem. In a second step, making use of symbolic computations, we arrive at the exact polynomial expression of the determinant of the algebraic problem matrix, allowing us to get high accuracy approximations of differential eigenvalues. View Full-Text
Keywords: eigenvalue differential problems; spectral methods; Sturm–Liouville problems eigenvalue differential problems; spectral methods; Sturm–Liouville problems
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Matos, J.M.A.; Rodrigues, M.J. Almost Exact Computation of Eigenvalues in Approximate Differential Problems. Math. Comput. Appl. 2019, 24, 96.

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