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Original Articles

Approximation in eigenvalue problems for holomorphic fredholm operator functions I

Pages 365-387 | Published online: 15 May 2007

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R. Pallav & A. Pedas. (2002) Quadratic spline collocation method for weakly singular integral equations and corresponding eigenvalue problem . Mathematical Modelling and Analysis 7:2, pages 285-296.
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Martin Halla. (2023) On the approximation of dispersive electromagnetic eigenvalue problems in two dimensions. IMA Journal of Numerical Analysis 43:1, pages 535-559.
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Gang Wang, Jian Meng, Ying Wang & Liquan Mei. (2022) A priori and a posteriori error estimates for a virtual element method for the non-self-adjoint Steklov eigenvalue problem . IMA Journal of Numerical Analysis 42:4, pages 3675-3710.
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Bo Gong, Jiguang Sun, Tiara Turner & Chunxiong Zheng. (2022) Finite element/holomorphic operator function method for the transmission eigenvalue problem. Mathematics of Computation.
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Xiangying Pang, Jiguang Sun & Zhimin Zhang. (2022) FE-holomorphic operator function method for nonlinear plate vibrations with elastically added masses. Journal of Computational and Applied Mathematics 410, pages 114156.
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Lothar Nannen & Markus Wess. (2022) Complex-scaled infinite elements for resonance problems in heterogeneous open systems. Advances in Computational Mathematics 48:2.
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Yingxia Xi & Xia Ji. (2022) A New Method using $$C^0$$IPG for the Biharmonic Eigenvalue Problem. Journal of Scientific Computing 90:3.
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Pavel S. Solov’ev, Diana M. Korosteleva & Sergey I. Solov’ev. 2022. Mesh Methods for Boundary-Value Problems and Applications. Mesh Methods for Boundary-Value Problems and Applications 475 491 .
Anna I. Repina, Alina O. Oktyabrskaya, Ilya V. Ketov & Evgenii M. Karchevskii. 2022. Mesh Methods for Boundary-Value Problems and Applications. Mesh Methods for Boundary-Value Problems and Applications 427 443 .
Stefan Kurz, Sebastian Schöps, Gerhard Unger & Felix Wolf. (2021) Solving Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. Mathematical Methods in the Applied Sciences 44:13, pages 10790-10803.
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Alexander O. Spiridonov, Anna I. Repina, Ilya V. Ketov, Sergey I. Solov’ev & Evgenii M. Karchevskii. (2021) Exponentially Convergent Galerkin Method for Numerical Modeling of Lasing in Microcavities with Piercing Holes. Axioms 10:3, pages 184.
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Gerhard Unger. (2021) Convergence analysis of a Galerkin boundary element method for electromagnetic resonance problems. Partial Differential Equations and Applications 2:3.
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Martin Halla. (2021) Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibility. Numerische Mathematik 148:2, pages 387-407.
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Wenqiang Xiao, Bo Gong, Jiguang Sun & Zhimin Zhang. (2021) Finite Element Calculation of Photonic Band Structures for Frequency Dependent Materials. Journal of Scientific Computing 87:1.
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Martin Halla. (2021) Analysis of Radial Complex Scaling Methods: Scalar Resonance Problems. SIAM Journal on Numerical Analysis 59:4, pages 2054-2074.
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Martin Halla. (2021) Electromagnetic Steklov eigenvalues: approximation analysis. ESAIM: Mathematical Modelling and Numerical Analysis 55:1, pages 57-76.
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Wenqiang Xiao, Bo Gong, Jiguang Sun & Zhimin Zhang. (2020) A new finite element approach for the Dirichlet eigenvalue problem. Applied Mathematics Letters 105, pages 106295.
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P. О. Savenko. (2020) Numerical Solution of a Two-Point Boundary-Value Problem for a System of Linear Differential Equations with Nonlinear Two-Dimensional Spectral Parameter. Journal of Mathematical Sciences 247:1, pages 73-87.
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Alexander O. Spiridonov, Alina Oktyabrskaya, Evgenii M. Karchevskii & Alexander I. Nosich. (2020) Mathematical and Numerical Analysis of the Generalized Complex-Frequency Eigenvalue Problem for Two-Dimensional Optical Microcavities. SIAM Journal on Applied Mathematics 80:4, pages 1977-1998.
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D. M. Korosteleva, L. N. Koronova, K. O. Levinskaya & S. I. Solov’ev. (2020) Finite difference approximation of eigenvibrations of a bar with oscillator. MATEC Web of Conferences 329, pages 03030.
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L. N. Koronova, D. M. Korosteleva, K. O. Levinskaya & S. I. Solov’ev. (2020) Eigenvibrations of a beam with two mechanical resonators attached to the ends. MATEC Web of Conferences 329, pages 03009.
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Spiridonov, Karchevskii & Nosich. (2019) Mathematical and Numerical Modeling of On-Threshold Modes of 2-D Microcavity Lasers with Piercing Holes. Axioms 8:3, pages 101.
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A. O. Spiridonov, E. M. Karchevskii & A. I. Nosich. (2018) Rigorous Formulation of the Lasing Eigenvalue Problem as a Spectral Problem for a Fredholm Operator Function. Lobachevskii Journal of Mathematics 39:8, pages 1148-1157.
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Martin Halla & Lothar Nannen. (2017) Two scale Hardy space infinite elements for scalar waveguide problems. Advances in Computational Mathematics 44:3, pages 611-643.
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Juan Carlos Araujo-Cabarcas, Christian Engström & Elias Jarlebring. (2018) Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map. Journal of Computational and Applied Mathematics 330, pages 177-192.
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Juan Carlos Araujo-Cabarcas & Christian Engström. (2017) On spurious solutions in finite element approximations of resonances in open systems. Computers & Mathematics with Applications 74:10, pages 2385-2402.
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A. A. Samsonov & S. I. Solov’ev. (2017) Eigenvibrations of a beam with load. Lobachevskii Journal of Mathematics 38:5, pages 849-855.
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Stefan Güttel & Françoise Tisseur. (2017) The nonlinear eigenvalue problem. Acta Numerica 26, pages 1-94.
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Olaf Steinbach & Gerhard Unger. (2016) Combined boundary integral equations for acoustic scattering‐resonance problems. Mathematical Methods in the Applied Sciences 40:5, pages 1516-1530.
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Christian Engström, Heinz Langer & Christiane Tretter. (2017) Rational eigenvalue problems and applications to photonic crystals. Journal of Mathematical Analysis and Applications 445:1, pages 240-279.
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S. I. Solov’ev. (2016) Eigenvibrations of a beam with elastically attached load. Lobachevskii Journal of Mathematics 37:5, pages 597-609.
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Christian Engström, Stefano Giani & Luka Grubišić. (2016) Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications. Computers & Mathematics with Applications 72:4, pages 952-973.
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Martin Halla. (2016) Convergence of Hardy Space Infinite Elements for Helmholtz Scattering and Resonance Problems. SIAM Journal on Numerical Analysis 54:3, pages 1385-1400.
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Thorsten Hohage & Lothar Nannen. (2014) Convergence of infinite element methods for scalar waveguide problems. BIT Numerical Mathematics 55:1, pages 215-254.
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Christian Engström. (2013) Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations. Numerische Mathematik 126:3, pages 413-440.
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A. Kimeswenger, O. Steinbach & G. Unger. (2014) Coupled Finite And Boundary Element Methods for Fluid-Solid Interaction Eigenvalue Problems. SIAM Journal on Numerical Analysis 52:5, pages 2400-2414.
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P. O. Savenko & L. P. Protsakh. (2012) Numerical solution of a two-point boundary-value problem with nonlinear two-dimensional spectral parameter. Journal of Mathematical Sciences 183:1, pages 43-53.
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O. Steinbach & G. Unger. (2012) Convergence Analysis of a Galerkin Boundary Element Method for the Dirichlet Laplacian Eigenvalue Problem. SIAM Journal on Numerical Analysis 50:2, pages 710-728.
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L. P. Protsakh & P. O. Savenko. (2010) Implicit-function methods for the solution of two-parameter linear spectral problems. Journal of Mathematical Sciences 170:5, pages 612-621.
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Petro Savenko & Myroslava Tkach. (2010) Numerical Approximation of Real Finite Nonnegative Function by the Modulus of Discrete Fourier Transform. Applied Mathematics 01:01, pages 65-75.
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Thomas Apel, Anna-Margarete Sändig & Sergey I. Solov'ev. (2003) Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes. ESAIM: Mathematical Modelling and Numerical Analysis 36:6, pages 1043-1070.
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