Výsledky vyhledávání - "method for computing eigenvalues and eigenfunctions"

A Boundary Shape Function Method for Computing Eigenvalues and Eigenfunctions of Sturm–Liouville Problems

Autoři: Chein-Shan Liu Jiang-Ren Chang Jian-Hung Shen a další

Zdroj: Mathematics, Vol 10, Iss 19, p 3689 (2022)

Témata: Sturm–Liouville problems, eigenvalues, shape function, canonical forms, boundary shape function method, Mathematics, QA1-939

Popis souboru: electronic resource

Relation: https://www.mdpi.com/2227-7390/10/19/3689; https://doaj.org/toc/2227-7390

Přístupová URL adresa: https://doaj.org/article/6f1ccc048f8d405f825d54192b019e66

On a method for computing eigenvalues and eigenfunctions of linear differential operators

Autoři: BRUSCHI, Mario CAMPOS R. G. PACE E.

Zdroj: Il Nuovo Cimento B Series 11. 105:131-163

Témata: 0103 physical sciences, 01 natural sciences

Přístupová URL adresa: https://link.springer.com/article/10.1007/BF02723074
http://ui.adsabs.harvard.edu/abs/1990NCimB.105..131B/abstract
https://link.springer.com/content/pdf/10.1007%2FBF02723074.pdf
https://hdl.handle.net/11573/99843

A Lie-Group Shooting Method for Computing Eigenvalues and Eigenfunctions of Sturm-Liouville Problems

Autoři: Chein-Shan Liu

Zdroj: Computer Modeling in Engineering & Sciences
Volume 26
Issue 3

Témata: Sturm-Liouville eigenvalues problem, Eigenvalue, Eigenfunction, Lie-group shooting method

Popis souboru: application/pdf

Přístupová URL adresa: https://www.techscience.com/doi/10.3970/cmes.2008.026.157.html

A Boundary Shape Function Method for Computing Eigenvalues and Eigenfunctions of Sturm–Liouville Problems.

Autoři: Liu, Chein-Shan Chang, Jiang-Ren Shen, Jian-Hung a další

Zdroj: Mathematics (2227-7390); Oct2022, Vol. 10 Issue 19, p3689, 22p

Témata: EIGENFUNCTIONS, ALGEBRAIC equations, EIGENVALUES, INITIAL value problems, NEUMANN boundary conditions

A Collocation Method for Computing Eigenvalues and Eigenfunctions of the Laplacian.

Autoři: WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER Reichel,Lothar

Zdroj: DTIC AND NTIS

Témata: Theoretical Mathematics, Numerical methods and procedures, Analytic functions, Computations, Harmonics, Approximation(Mathematics), Eigenvalues, Eigenvectors, Points(Mathematics), Boundaries, Boundary value problems, Boundary collocation method, Text

URL: https://apps.dtic.mil/docs/citations/ADA132827

A Collocation Method for Computing Eigenvalues and Eigenfunctions of the Laplacian.

Autoři: Reichel,Lothar WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Přispěvatelé: Reichel,Lothar WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Zdroj: DTIC AND NTIS

Témata: Theoretical Mathematics, Numerical methods and procedures, Analytic functions, Computations, Harmonics, Approximation(Mathematics), Eigenvalues, Eigenvectors, Points(Mathematics), Boundaries, Boundary value problems, Boundary collocation method

Popis souboru: text/html

Relation: http://www.dtic.mil/docs/citations/ADA132827

Dostupnost: http://www.dtic.mil/docs/citations/ADA132827
http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA132827

Computation of eigenfunctions and eigenvalues for the Sturm-Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint.

Autoři: Khapaev, M. Khapaeva, T.

Zdroj: Computational Mathematics & Mathematical Physics. Oct2016, Vol. 56 Issue 10, p1732-1736. 5p.

Témata: *STURM-Liouville equation, *EIGENFUNCTIONS, *EIGENVALUES, *BOUNDARY value problems, *NEUMANN boundary conditions

Generalization Error Estimates of Machine Learning Methods for Solving High Dimensional Schr\'odinger Eigenvalue Problems

Autoři: Yu, Hao Guo, Yixiao Ming, Pingbing

Témata: Mathematics - Numerical Analysis, text

URL: http://arxiv.org/abs/2408.13511

Surface Eigenvalues with Lattice-Based Approximation In comparison with analytical solution

Autoři: Wu, Yingying Wu, Tianqi Yau, Shing-Tung

Témata: Mathematics - Numerical Analysis, text

URL: http://arxiv.org/abs/2203.03603

A CONVERGENT ADAPTIVE METHOD FOR ELLIPTIC EIGENVALUE PROBLEMS.

Autoři: Giani, S. Graham, I. G.

Zdroj: SIAM Journal on Numerical Analysis; 2009, Vol. 47 Issue 2, p1067-1091, 25p, 2 Diagrams, 8 Charts, 3 Graphs

Témata: FINITE element method, ELLIPTIC functions, EIGENVALUES, NUMERICAL solutions to integral equations, NUMERICAL analysis, BILINEAR transformation method

The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula

Autoři: Liu, Chein-Shan Li, Botong

Témata: keyword:symmetric Sturm-Liouville problem, keyword:inverse potential problem, keyword:special matrix eigenvalue problem, keyword:product formula, keyword:fictitious time integration method, msc:34A55, msc:34B24

Popis souboru: application/pdf

Relation: mr:MR4747497; zbl:Zbl 07893340; reference:[1] Andrew, A. L.: Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions.J. Comput. Appl. Math. 125 (2000), 359-366. Zbl 0970.65086, MR 1803202, 10.1016/S0377-0427(00)00479-9; reference:[2] Borg, G.: Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe.Acta Math. 78 (1946), 1-96 German. Zbl 0063.00523, MR 0015185, 10.1007/BF02421600; reference:[3] Çelik, I.: Approximate calculation of eigenvalues with the method of weighted residuals-collocation method.Appl. Math. Comput. 160 (2005), 401-410. Zbl 1064.65073, MR 2102818, 10.1016/j.amc.2003.11.011; reference:[4] Çelik, I.: Approximate computation of eigenvalues with Chebyshev collocation method.Appl. Math. Comput. 168 (2005), 125-134. Zbl 1082.65555, MR 2170019, 10.1016/j.amc.2004.08.024; reference:[5] Dehghan, M.: An efficient method to approximate eigenfunctions and high-index eigenvalues of regular Sturm-Liouville problems.Appl. Math. Comput. 279 (2016), 249-257. Zbl 1410.65276, MR 3458019, 10.1016/j.amc.2016.01.026; reference:[6] Ghelardoni, P.: Approximations of Sturm-Liouville eigenvalues using boundary value methods.Appl. Numer. Math. 23 (1997), 311-325. Zbl 0877.65056, MR 1445127, 10.1016/S0168-9274(96)00073-6; reference:[7] Ghelardoni, P., Magherini, C.: BVMs for computing Sturm-Liouville symmetric potentials.Appl. Math. Comput. 217 (2010), 3032-3045. Zbl 1204.65092, MR 2733748, 10.1016/j.amc.2010.08.036; reference:[8] Gould, S. H.: Variational Methods for Eigenvalue Problems: An Introduction to the Methods of Rayleigh, Ritz, Weinstein, and Aronszajn.Dover, New York (1995). Zbl 0077.09603, MR 1350533, 10.3138/9781487596002; reference:[9] Hald, O. H.: The inverse Sturm-Liouville problem and the Rayleigh-Ritz method.Math. Comput. 32 (1978), 687-705. Zbl 0432.65050, MR 0501963, 10.1090/S0025-5718-1978-0501963-2; reference:[10] Hald, O. H.: The inverse Sturm-Liouville problem with symmetric potentials.Acta Math. 141 (1978), 263-291. Zbl 0431.34013, MR 0505878, 10.1007/BF02545749; reference:[11] Hinton, D., (Eds.), P. W. Schaefer: Spectral Theory & Computational Methods of Sturm-Liouville Problems.Lecture Notes in Pure and Applied Mathematics 191. Marcel Dekker, New York (1997). Zbl 0866.00046, MR 1460546; reference:[12] Kobayashi, M.: Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials.Comput. Math. Appl. 18 (1989), 357-364. Zbl 0682.65054, MR 0999264, 10.1016/0898-1221(89)90220-4; reference:[13] Liu, C.-S.: A Lie-group shooting method for computing eigenvalues and eigenfunctions of Sturm-Liouville problems.CMES, Comput. Model. Eng. Sci. 26 (2008), 157-168. Zbl 1232.65110, MR 2426635, 10.3970/cmes.2008.026.157; reference:[14] Liu, C.-S.: Analytic solutions of the eigenvalues of Mathieu's equation.J. Math. Research 12 (2020), Article ID p1, 11 pages. 10.5539/jmr.v12n1p1; reference:[15] Liu, C.-S.: Accurate eigenvalues for the Sturm-Liouville problems, involving generalized and periodic ones.J. Math. Res. 14 (2022), Article ID p1, 19 pages. 10.5539/jmr.v14n4p1; reference:[16] Liu, C.-S., Atluri, S. N.: A novel fictitious time integration method for solving the discretized inverse Sturm-Liouville problems, for specified eigenvalues.CMES, Comput. Model. Eng. Sci. 36 (2008), 261-285. Zbl 1232.74007, MR 2489473, 10.3970/cmes.2008.036.261; reference:[17] Liu, C.-S., Atluri, S. N.: A novel time integration method for solving a large system of non-linear algebraic equations.CMES, Comput. Model. Eng. Sci. 31 (2008), 71-83. Zbl 1152.65428, MR 2450570; reference:[18] Liu, C.-S., Chang, J.-R., Shen, J.-H., Chen, Y.-W.: A boundary shape function method for computing eigenvalues and eigenfunctions of Sturm-Liouville problems.Mathematics 10 (2022), Article ID 3689, 22 pages. 10.3390/math10193689; reference:[19] Liu, C.-S., Li, B.: An upper bound theory to approximate the natural frequencies and parameters identification of composite beams.Composite Struct. 171 (2017), 131-144. 10.1016/j.compstruct.2017.03.014; reference:[20] Liu, C.-S., Li, B.: Reconstructing a second-order Sturm-Liouville operator by an energetic boundary function iterative method.Appl. Math. Lett. 73 (2017), 49-55. Zbl 1375.65100, MR 3659907, 10.1016/j.aml.2017.04.023; reference:[21] Liu, C.-S., Li, B.-T.: An $R(x)$-orthonormal theory for the vibration performance of non-smooth symmetric composite beam with complex interface.Acta Mech. Sin. 35 (2019), 228-241. MR 3908891, 10.1007/s10409-018-0799-3; reference:[22] Brunt, B. van: The Calculus of Variations.Universitext. Springer, New York (2004). Zbl 1039.49001, MR 2004181, 10.1007/b97436; reference:[23] Berghe, G. Vanden, Daele, M. Van: Exponentially-fitted Numerov methods.J. Comput. Appl. Math. 200 (2007), 140-153. Zbl 1110.65071, MR 2276821, 10.1016/j.cam.2005.12.022

Dostupnost: http://hdl.handle.net/10338.dmlcz/152354

RIGOROUS ENVELOPE APPROXIMATION FOR INTERFACE WAVE PACKETS IN MAXWELL'S EQUATIONS WITH TWO DIMENSIONAL LOCALIZATION.

Autoři: DOHNAL, TOMÁŠ SCHNAUBELT, ROLAND TIETZ, DANIEL P.

Zdroj: SIAM Journal on Mathematical Analysis; 2023, Vol. 55 Issue 6, p6898-6939, 43p

Témata: WAVE packets, MAXWELL equations, SOBOLEV spaces, EQUATIONS, DIELECTRIC materials, PROBLEM solving, METAL-insulator transitions

An estimation of the eigenfunctions of periodic Sturm-Liouville problems.

Autoři: Dinibutun, Seza

Zdroj: Arab Journal of Basic & Applied Sciences; Dec 2021, Vol. 28 Issue 1, p107-112, 6p

Témata: EIGENFUNCTIONS, STURM-Liouville equation, BOUNDARY value problems, PARTIAL differential equations, HEAT equation

Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials.

Autoři: Bihun, Oksana Mourning, Clark

Zdroj: Advances in Mathematical Physics; 2/7/2018, p1-10, 10p

Témata: ORTHOGONAL polynomials, DIFFERENTIAL operators, NONLINEAR theories, ZERO (The number), HERMITE polynomials

A convergent adaptive method for elliptic eigenvalue problems

Autoři: S. Giani I. G. Graham The Pennsylvania State University CiteSeerX Archives

Přispěvatelé: S. Giani I. G. Graham The Pennsylvania State University CiteSeerX Archives

Zdroj: http://www.newton.ac.uk/preprints/NI07054.pdf.

Témata: Second-order Elliptic Problems, Eigenvalues, Adaptive finite element methods

Popis souboru: application/pdf

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.830; http://www.newton.ac.uk/preprints/NI07054.pdf

Dostupnost: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.830
http://www.newton.ac.uk/preprints/NI07054.pdf

Reconstruction of moving boundary for one-dimensional heat conduction equation by using the Lie-group shooting method.

Autoři: Liu, Chein-Shan

Zdroj: Inverse Problems in Science & Engineering; Apr2012, Vol. 20 Issue 3, p311-334, 24p, 7 Graphs

Témata: INVERSE problems, HEAT conduction, HEAT equation, LIE groups, BOUNDARY value problems, ITERATIVE methods (Mathematics), NUMERICAL integration

The Lie-Group Shooting Method for Solving Multi-dimensional Nonlinear Boundary Value Problems.

Autoři: Liu, Chein-Shan

Zdroj: Journal of Optimization Theory & Applications; Feb2012, Vol. 152 Issue 2, p468-495, 28p

Témata: LIE groups, NUMERICAL solutions to nonlinear boundary value problems, NUMERICAL solutions to boundary value problems, RUNGE-Kutta formulas, DUFFING equations, LIE algebras

The theory of regularized traces of Sturm-Liouville operators as applied to approximate calculation of eigenvalues and eigenfunctions of certain singular operators.

Autoři: Kerimov, M.

Zdroj: Computational Mathematics & Mathematical Physics; Dec2011, Vol. 51 Issue 12, p2079-2101, 23p

Témata: EIGENVALUES, MATRICES (Mathematics), JACOBI method, WEYL'S problem, DIFFERENTIAL operators

Numerical Kähler-Einstein Metric on the Third del Pezzo.

Autoři: Doran, Charles Headrick, Matthew Herzog, Christopher a další

Zdroj: Communications in Mathematical Physics; Aug2008, Vol. 282 Issue 2, p357-393, 37p, 2 Diagrams, 15 Graphs

Témata: MONGE-Ampere equations, ALGORITHMS, RICCI flow, CALABI-Yau manifolds, LAPLACIAN operator, EIGENVALUES

Stability results for convection in thawing subsea permafrost.

Autoři: Budu, Paula

Zdroj: Continuum Mechanics & Thermodynamics; Aug2001, Vol. 13 Issue 4, p269-285, 17p