64
with K. Nagatou, M. T. Nakao, and Y. Watanabe: A computer-assisted stability proof for the Orr-Sommerfeld problem with Poiseuille flow. Nonlinear Theory and Its Applications, IEICE 2, 123-127 (2011).
63.
with K. Nagatou and M. T. Nakao: Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators. Proc. R. Soc. A, 19 pp.,
published online before print 10.2011: doi: 10.1098/rspa.2011.0159; pdf
62.
with T. Dohnal and W. Reichel: Surface gap soliton ground states for the nonlinear Schrödinger equation. Comm. Math. Phys., Volume 308, Issue 2 (2011), 511-542; http://www.springerlink.com/content/j01k11547j2p8083/ - pdf
61.
with W. Dörfler, A. Lechleiter, G. Schneider, and Ch. Wieners: Photonic Crystals: Mathematical Analysis and Numerical Approximation. Birkh"auser, 2010; Oberwolfach Seminars 42.
60.
with T. Dohnal and W. Reichel: Localized modes of the linear periodic Schrödinger operator with a nonlocal perturbation. SIAM J. Math. Anal., Volume 41, Issue 5 (2009), 1967-1993. pdf
59.
with B. M. Brown, V. Hoang, I. G. Wood: Floquet-Bloch Theory for Elliptic Problems with Discontinuous Coefficients. In: Janas et al. (eds.), Spectral Theory and Analysis, Proceedings of OPTAMP 2008 (to appear in: Operator Theory: Advances and Applications, Birkhäuser).
58.
with P. J. McKenna, F. Pacella, D. Roth: A Uniqueness Result for a Semilinear Elliptic Problem: A Computer-assisted Proof. J. Differential Equations 247 (2009) 2140-2162; doi:10.1016/j.jde.2009.06.023.
57.
Computer-assisted Proofs for Semilinear Elliptic Boundary Value Problems. Japan Journal for Industrial and Applied Mathematics, Vol. 26, No. 2-3 (2009); doi: 10.1007/BF03186542.
56.
with T. Dohnal, W. Reichel: Localized Modes of the Linear Periodic Schrödinger Operator with a Nonlocal Perturbation. SIAM J. Math. Anal., Volume 41, Issue 5 (2009), 1967-1993.
55.
with V. Hoang, Ch. Wieners: A computer-assisted proof for photonic band gaps. Z. angew. Math. Phys., DOI 10.1007/s00033-008-8021-2 (2009); www.birkhauser.ch/ZAMP.
54.
with B. M. Brown, V. Hoang, I.G. Wood: On Spectral Bounds for Photonic Crystal Waveguides. In: Inequalities and Applications (C. Bandle, A. Gilànyi, L. Losonczi, Z. Pales, M. Plum eds.), International Series of Numerical Mathematics, Vol. 157, 23-30 (2009).
53.
with Y. Watanabe, M. T. Nakao: A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow. Z. Angew. Math. Mech. 89, No. 1, 5-18 (2009)/DOI 10.1002/zamm.200700158.
52.
Existence and Multiplicity Proofs for Semilinear Elliptic Boundary Value Problems by Computer Assistance. DMV Jahresbericht: JB 110, Band (2008), Heft 1, 19-54.
Download: emp.ps
51.
mit W. N. Everitt, L. Markus, M. Muzzulini: A continuum of unusual selfadjoint linear partial differential operators.
Journal of Computational and Applied Mathematics 208, 164-175 (2007).
50.
with Ch. Wieners: Numerical enclosures for variational inequalities. Computational Methods in Applied Mathematics, Vol. 7, No. 4, 376-388 (2007).
49.
with B. Breuer, J. Horak, P.J. McKenna: A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam.
Submitted
Download: travelling.pdf
48.
with R. C. Brown: An Opial Type Inequality with an Integral Boundary Condition.
To appear in Proc. R. Soc. Lond. A.
Download: opial_type.pdf
47.
with W.N. Everitt, L. Markus: An Unusual Self-Adjoint Linear Partial Differential Operator.
Trans. Amer. Math. Soc. 367, 1303-1324 (2005).
Download: self-adjoint.pdf
46.
with E. B. Davies: Spectral Pollution.
IMA Journal of Numerical Analysis 24, 417-438 (2004).
45.
with B. Breuer, P.J. McKenna: Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
J. Differential Equations 195, 243-269 (2003).
44.
with B.M. Brown, W.D. Evans: Titchmarsh-Sims-Weyl theory for Complex Hamiltonian Systems.
Proc. London Math. Soc. (3) 87, 419-450 (2003).
Download: titchmarsh.pdf
43.
with J.-R. Lahmann: A computer-assisted instability proof for the Orr-Sommerfeld equation with Blasius profile.
ZAMM 84, No. 3, 188-204 (2004).
Download: orr-sommerfeld.pdf
42.
with E. Adams: Free Vibrations of Trusses by Fourier Decomposition, and Homotopy Methods for Nonlinear Matrix Eigenvalue Problems, I and II.
J. Math. Anal. Appl. 275, 333-353 (2002) and 276, 64-79 (2002).
41.
with Ch. Wieners: New solutions of the Gelfand problem.
J. Math. Anal. Appl. 269, 588-606 (2002).
40.
with Ch. Wieners: Optimal a priori estimates for interface problems.
Numer. Math. 95, 735-759 (2003).
39.
with P. J. McKenna: Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
J. Math. Anal. Appl. 251, No. 2, 710-715 (2000).
38.
with B. Breuer, P.J. McKenna: Inclusions and Existence Proofs for Solutions of a Nonlinear Boundary Value Problem by Spectral Numerical Methods.
Computing Suppl. 15, 61-77 (2001).
37.
with Ch. Hipp: Optimal investment for investors with state dependent income, and for insurers.
Finance and Stochastics, Vol. 7, No. 3, 299-321 (2003).
36.
Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems.
In: Symbolic Algebraic Methods and Verification Methods (Eds.: G. Alefeld, J. Rohn, S. Rump, T. Yamamoto), Springer Wien New York, 195-207 (2001).
35.
with Ch. Hipp: Optimal investment for insurers.
Insurance, Mathematics and Economics 27, 215-228 (2000).
34.
with H. Behnke, U. Mertins, Ch. Wieners: Eigenvalue inclusions via domain decomposition.
Proc. R. Soc. Lond. A. 456, 2717-2730 (2000).
33.
Computer-assisted Enclosure Methods for Elliptic Differential Equations.
Linear Algebra and its Applications 324, 147-187 (2001).
32.
with J. Lahmann: Das Spektrum der Orr-Sommerfeld-Gleichung mit Blasius-Strömungsprofil.
ZAMM 78, Suppl. 3, S987 - S988 (1998).
31.
with B. Breuer: Lösungseinschließungen bei einem nichtlinearen Randwertproblem mittels eines Fourierreihenansatzes.
Internal Report.
30.
with R. M. Redheffer: A Class of Second-order Differential Equations.
J. Differential Equations 154, 454-469 (1999).
29.
with J. Lahmann: On the spectrum of the Orr-Sommerfeld equation on the semi-axis.
Math. Nachr. 216, 145-153 (2000).
28.
with B.M. Brown, D.K.R. McCormack, W.D. Evans: On the spectrum of second order differential operators with complex coeficients.
Proc. Royal Soc. London. A 455, 1235-1257 (1999).
27.
with B.M. Brown, M.S.P. Eastham, D.K.R. McCormack: On a new algorithm for the computation of enclosures for the Titchmarsh-Weyl m-function.
Result. Math. 33, 50-64 (1998).
26.
Eigenvalue Problems for Differential Equations.
In: Wavelets, Multilevel Methods and Elliptic PDEs (Eds.: M. Ainsworth , J. Levesley, M. Marletta, W.A. Light), Clarendon Press, Oxford, 39-83 (1997).
25.
Guaranteed Numerical Bounds for Eigenvalues.
In: Spectral theory and computational methods of Sturm-Liouville problems (Eds.: D. Hinton, P. Schaefer), Marcel Dekker, New York, 313-332 (1997).
24.
Enclosure Methods with Existence Proof for Elliptic Differential Equations. Proceedings zu "General Inequalities 7" (Oberwolfach 1995), International Series of Numerical Mathematics, Vol. 123, 347-368 (1997).
23.
Enclosures for Two-Point Boundary Value Problems near Bifurcation Points.
In: Scientific Computing and Validated Numerics, Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN-95, held in Wuppertal, Germany, September 26-29, 1995 (Eds.: G. Alefeld, A. Frommer, B. Lang), Mathematical Research, Volume 90, Akademie Verlag, 265-279 (1996).
22.
Existence Proofs for Elliptic Boundary Value Problems by Numerical Means.
ZAMM 75 SII, S429-S432 (1995).
21.
Lösungseinschließung mit automatischem Existenzbeweis bei elliptischen Randwertproblemen.
In: Jahrbuch Überblicke Mathematik 1995 (Hrsg.: A. Beutelspacher, S.D. Chatterji, U. Kulisch, R. Liedl), Vieweg, Braunschweig, 103 - 124 (1995).
20.
Enclosures for Weak Solutions of Nonlinear Elliptic Boundary Value Problems.
In: Inequalities and Applications (Ed.: Ravi P. Agarwal), World Scientific Series In Applicable Analysis, Vol. 3, 505-521 (1994).
19.
Inclusion Methods for Elliptic Boundary Value Problems.
In: Topics in Validated Computations (Ed.: J. Herzberger), Studies in Computational Mathematics 5, North Holland (Elsevier), Amsterdam, 323 - 379 (1994).
18.
Existence and Enclosure Results for Continua of Solutions of Parameter-Dependent Nonlinear Boundary Value Problems.
Journal of Computational and Applied Mathematics 60, 187 - 200 (1995).
17.
with B. Kalkofen: Optimal Pricing Rules for Private-Value Auctions with Incomplete Information.
Ifo-Studien 1/1996, 77 - 100.
16.
Enclosures for Solutions of Parameter-dependent Nonlinear Elliptic Boundary Value Problems: Theory and Implementation on a Parallel Computer.
Interval Computations 3 (Special Issue on Parallel Algorithms), 106 - 121 (1994).
15.
with B.M. Brown, W.D. Evans und V.G. Kirby: Safe numerical bounds for the Titchmarsh-Weyl m-function.
Mathematical Proceedings of the Cambridge Philosophical Society 113, 583-599 (1993).
14.
An Existence and Inclusion Method for Two-Point Boundary Value Problems with Turning Points.
ZAMM 74, 615 - 623 (1994).
13.
Numerical Existence Proofs and Explicit Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems.
Computing 49, 25-44 (1992).
12.
Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information.
International Journal of Game Theory 20, 393-418 (1992).
11.
Continuous Sealed-bid Auctions with Asymmetric Incomplete Information.
Methods of Operations Research 63, 303-312.
10.
Bounds for eigenvalues of second-order elliptic differential operators.
ZAMP 42, 848 - 863 (1991).
9.
Existence proofs in combination with error bounds for approximate solutions of weakly nonlinear second-order elliptic boundary value problems.
ZAMM 71, T 660 - T 662 (1991).
8.
Explicit H2-estimates and pointwise bounds for solutions of second-order elliptic boundary value problems.
J. Math. Anal. Appl. 165, 36-61 (1992).
7.
Computer-assisted existence proofs for two-point boundary value problems.
Computing 46, 19-34 (1991).
6.
Verified existence and inclusion results for two-point boundary value problems.
IMACS Annals on Computing and Applied Mathematics, Baltzer, Vol. 7, 341-355 (1990).
5.
with M. Göhlen und J. Schröder: A Programmed Algorithm for Existence Proofs for Two-Point Boundary Value Problems.
Computing 44, 91-132 (1990).
4.
Existence and inclusion for two-point boundary value problems by numerical means.
In: Computational Ordinary Differential Equations (Eds.: J. R. Cash, I. Gladwell), Clarendon Press, Oxford, 415-423 (1992).
3.
Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method.
ZAMP 41, 205-226 (1990).
2.
Shape-Invariant Bounds for Reaction-Diffusion Systems with Unequal Diffusion Coeficients.
J. Differential Equations 73, 82-103 (1988).
1.
Pointwise Bounds for Linear Reaction-Diffusion Systems and an Extension to Nonlinear Problems.
J. Math. Anal. Appl. 135, 88-111 (1988).