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Solving differential eigenproblems via the spectral Tau method

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Solving differential eigenproblems via the spectral Tau method

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Vasconcelos, PB.; Roman, JE.; Matos, JMA. (2023). Solving differential eigenproblems via the spectral Tau method. Numerical Algorithms. 92:1789-1811. https://doi.org/10.1007/s11075-022-01366-z

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Título: Solving differential eigenproblems via the spectral Tau method
Autor: Vasconcelos, P. B. Roman, Jose E. Matos, J. M. A.
Entidad UPV: Universitat Politècnica de València. Escola Tècnica Superior d'Enginyeria Informàtica
Fecha difusión:
Resumen:
[EN] The spectral Tau method to compute eigenpairs of ordinary differential equations is implemented as part of the Tau Toolbox-a numerical library for the solution of integro-differential problems. This mathematical ...[+]
Palabras clave: Spectral methods , Differential eigenproblems , Algebraic eigenvalue problems
Derechos de uso: Reserva de todos los derechos
Fuente:
Numerical Algorithms. (issn: 1017-1398 )
DOI: 10.1007/s11075-022-01366-z
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s11075-022-01366-z
Código del Proyecto:
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107379RB-I00/ES/ALGORITMOS PARALELOS Y SOFTWARE PARA METODOS ALGEBRAICOS EN ANALISIS DE DATOS/
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00144%2F2020/PT
Agradecimientos:
This work was partially supported by the Spanish Agencia Estatal de Investigacion under grant PID2019-107379RB-I00/AEI/10.13039/501100011033, and by CMUP, which is financed by national funds through FCT-Fundacao para a ...[+]
Tipo: Artículo

References

Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., Van Der Vorst, H.: Templates for the solution of algebraic eigenvalue problems: a practical guide. SIAM (2000). https://doi.org/10.1137/1.9780898719581

Bailey, P.B., Everitt, W.N., Zettl, A.: Algorithm 810: the sleign2 Sturm-Liouville code. ACM Trans. Math. Softw. 27(2), 143–192 (2001). https://doi.org/10.1145/383738.383739

Boyd, J.: Chebyshev and Fourier spectral methods. Dover publications Inc (2000) [+]
Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., Van Der Vorst, H.: Templates for the solution of algebraic eigenvalue problems: a practical guide. SIAM (2000). https://doi.org/10.1137/1.9780898719581

Bailey, P.B., Everitt, W.N., Zettl, A.: Algorithm 810: the sleign2 Sturm-Liouville code. ACM Trans. Math. Softw. 27(2), 143–192 (2001). https://doi.org/10.1145/383738.383739

Boyd, J.: Chebyshev and Fourier spectral methods. Dover publications Inc (2000)

Bridges, T.J., Morris, P.J.: Differential eigenvalue problems in which the parameter appears nonlinearly. J. Comput. Phys. 55(3), 437–460 (1984). https://doi.org/10.1016/0021-9991(84)90032-9

Butler, K.M., Farrell, B.F.: Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A-Fluid 4(8), 1637–1650 (1992). https://doi.org/10.1063/1.858386

Charalambides, M., Waleffe, F.: Gegenbauer Tau methods with and without spurious eigenvalues. SIAM J. Numer. Anal. 47(1), 48–68 (2009). https://doi.org/10.1137/070704228

Chaves, T., Ortiz, E.L.: On the numerical solution of two-point boundary value problems for linear differential equations. Z Angew Math. Mech. 48(6), 415–418 (1968). https://doi.org/10.1002/zamm.19680480607

Dawkins, P.T., Dunbar, S.R., Douglass, R.W.: The origin and nature of spurious eigenvalues in the spectral Tau method. J. Comput. Phys. 147 (2), 441–462 (1998). https://doi.org/10.1006/jcph.1998.6095

Dongarra, J., Straughan, B., Walker, D.: Chebyshev Tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. Appl. Numer. Math. 22(4), 399–434 (1996). https://doi.org/10.1016/S0168-9274(96)00049-9

Driscoll, T.A., Hale, N.: Rectangular spectral collocation. IMA J. Numer. Anal. 36(1), 108–132 (2016). https://doi.org/10.1093/imanum/dru062

Driscoll, T.A., Hale, N., Trefethen, L.N.: Chebfun Guide (2014)

Gardner, D.R., Trogdon, S.A., Douglass, R.W.: A modified Tau spectral method that eliminates spurious eigenvalues. J. Comput. Phys. 80(1), 137–167 (1989). https://doi.org/10.1016/0021-9991(89)90093-4

Gheorghiu, C.I.: Accurate spectral collocation computation of high order eigenvalues for singular Schrödinger equations. Computation 9(2), 2 (2021). https://doi.org/10.3390/computation9010002

Gheorghiu, C.I., Pop, I.S.: A modified chebyshev-tau method for a hydrodynamic stability problem. In: Stancu, D.D. (ed.) Approximation and optimization. Transilvania Press, Cluj-Napoca, pp. 119–126 (1996)

Gheorghiu, C.I., Rommes, J.: Application of the Jacobi-Davidson method to accurate analysis of singular linear hydrodynamic stability problems. Int. J. Numer. Methods Fluids 71(3), 358–369 (2012). https://doi.org/10.1002/fld.3669

Greenberg, L., Marletta, M.: Algorithm 775: the code SLEUTH for solving fourth-order Sturm-Liouville problems. ACM T. Math. Softw. 23(4), 453–493 (1997). https://doi.org/10.1145/279232.279231

Güttel, S., Tisseur, F.: The nonlinear eigenvalue problem. Acta Numerica 26, 1–94 (2017). https://doi.org/10.1017/S0962492917000034

Güttel, S., van Beeumen, R., Meerbergen, K., Michiels, W.: NLEIGS: a class of fully rational Krylov methods for nonlinear eigenvalue problems. SIAM J. Sci. Comput. 36(6), A2842–A2864 (2014). https://doi.org/10.1137/130935045

Hammarling, S., Munro, C.J., Tisseur, F.: An algorithm for the complete solution of quadratic eigenvalue problems. ACM T. Math. Softw. 39(3), 1–19 (2013). https://doi.org/10.1145/2450153.2450156

Lanczos, C.: Trigonometric interpolation of empirical and analytical functions. J. Math. Phys. 17(1–4), 123–199 (1938). https://doi.org/10.1002/sapm1938171123

Ledoux, V., Daele, M.V., Berghe, G.V.: Matslise: a MATLAB package for the numerical solution of Sturm-Liouville and schrödinger equations. ACM Trans. Math. Softw. (TOMS) 31(4), 532–554 (2005). https://doi.org/10.1145/1114268.1114273

Malik, M., Huy, D.H.: Vibration analysis of continuous systems by differential transformation. Appl. Math. Comput. 96(1), 17–26 (1998). https://doi.org/10.1016/S0096-3003(97)10076-5

Matos, J.M.A., Rodrigues, M.J., Matos, J.C.: Explicit formulae for integro-differential operational matrices. Math. Comput. Sci. 15, 45–61 (2021). https://doi.org/10.1007/s11786-020-00465-1

McFadden, G.B., Murray, B.T., Boisvert, R.F.: Elimination of spurious eigenvalues in the Chebyshev Tau spectral method. J. Comput. Phys. 91(1), 228–239 (1990). https://doi.org/10.1016/0021-9991(90)90012-P

Moler, C.B., Stewart, G.W.: An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10(2), 241–256 (1973). https://doi.org/10.1137/0710024

Olver, S., Townsend, A.: A fast and well-conditioned spectral method. SIAM Rev. 55(3), 462–489 (2013). https://doi.org/10.1137/120865458

Orszag, S.A.: Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50 (04), 689 (1971). https://doi.org/10.1017/S0022112071002842

Ortiz, E.L., Samara, H.: An operational approach to the Tau method for the numerical solution of non-linear differential equations. Computing 27, 15–26 (1981). https://doi.org/10.1007/BF02243435

Ortiz, E.L., Samara, H.: Numerical solution of differential eigenvalue problems with an operational approach to the Tau method. Computing 31(2), 95–103 (1983). https://doi.org/10.1007/BF02259906

Pruess, S., Fulton, C.T.: Mathematical software for Sturm-Liouville problems. ACM Trans. Math. Softw. (TOMS) 19(3), 360–376 (1993). https://doi.org/10.1145/155743.155791

Pryce, J.D.: Error control of phase-function shooting methods for Sturm-Liouville problems. IMA J. Numer. Anal. 6(1), 103–123 (1986). https://doi.org/10.1093/imanum/6.1103

Pryce, J.D., Marletta, M.: A new multi-purpose software package for Schrödinger and Sturm-Liouville computations. Comput. Phys. Commun. 62(1), 42–52 (1991). https://doi.org/10.1016/0010-4655(91)90119-6

Reddy, S.C., Henningson, D.S.: Energy growth in viscous channel flows. J. Fluid Mech. 252, 209–238 (1993). https://doi.org/10.1017/S0022112093003738

Reddy, S.C., Schmid, P.J., Henningson, D.S.: Pseudospectra of the Orr–Sommerfeld operator. SIAM J. Appl. Math. 53(1), 15–47 (1993). https://doi.org/10.1137/0153002

Rommes, J.: Arnoldi and Jacobi-Davidson methods for generalized eigenvalue problems Ax = λBx with singular B. Math. Comput. 77 (262), 995–1016 (2007). https://doi.org/10.1090/s0025-5718-07-02040-6

Solov’ëv, S.I.: Preconditioned Iterative methods for a class of nonlinear eigenvalue problems. Linear Algebra Appl. 415(1), 210–229 (2006 ). https://doi.org/10.1016/j.laa.2005.03.034

Tisseur, F., Higham, N.J.: Structured pseudospectra for polynomial eigenvalue problems, with applications. SIAM J. Matrix Anal. Appl. 23(1), 187–208 (2001). https://doi.org/10.1137/S0895479800371451

Trindade, M., Matos, J., Vasconcelos, P.B.: Towards a Lanczos’ τ-method toolkit for differential problems. Math Comp. Sci. 10(3), 313–329 (2016). https://doi.org/10.1007/s11786-016-0269-x

Yuan, S., Ye, K., Xiao, C., Kennedy, D., Williams, F.: Solution of regular second-and fourth-order Sturm-Liouville problems by exact dynamic stiffness method analogy. J. Eng. Math. 86(1), 157–173 (2014). https://doi.org/10.1007/s10665-013-9646-5

Zebib, A.: Removal of spurious modes encountered in solving stability problems by spectral methods. J. Comput. Phys. 70(2), 521–525 (1987). https://doi.org/10.1016/0021-9991(87)90193-8

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