Asymptotically correct error estimation for collocation methods applied to singular boundary value problems

Othmar Koch

Type: Article

Publication Date: 2005-05-31

Citations: 37

DOI: https://doi.org/10.1007/s00211-005-0617-2

View

Locations

Numerische Mathematik - View

Similar Works

Action	Title	Year	Authors
+	Asymptotic Accuracy and Convergence for Point Collocation Methods	1985	Wolfgang L. Wendland
+	Asymptotic Accuracy and Convergence for Point Collocation Methods	1985	Wolfgang L. Wendland
+	Optimality of theoretical error estimates for spline collocation methods for linear weakly singular Volterra integro-differential equations	2005	Inga Parts
+ PDF Chat	Uniform Convergence Estimates for a Collocation Method for the Cauchy Singular Integral Equation	1997	Maria Rosaria Capobianco Maria Grazia Russo
+	Collocation algorithms and error analysis for approximate solutions of ordinary differential equations	1981	A. H. Ahmed
+	Error analysis of collocation methods for the numerical solution of ordinary differential equations	1974	D. M. Cruickshank
+	Asymptotic error expansion of a collocation-type method for Volterra-Hammerstein integral equations	1993	Guoqiang Han
+	Convergence of a collocation method for ordinary differential equations	1967	Yu. P. Yartsev
+	Asymptotic error expansion of a collocation-type method for Hammerstein equations	1995	Guoqiang Han Zhang Liqing
+	The Fine Error Estimation of Collocation Methods on Uniform Meshes for Weakly Singular Volterra Integral Equations	2020	Hui Liang Hermann Brunner
+	Fourth order accuracy collocation method for singularly perturbed boundary value problems	1992	I. A. Blatov V. V. Strygin
+ PDF Chat	Convergence analysis of oversampled collocation boundary element methods in 2D	2022	Georg Maierhofer Daan Huybrechs
+	A uniformly accurate spline collocation method for a singular perturbation problem	1990	Mirjana D. Stojanović
+	Efficient mesh selection for collocation methods applied to singular BVPs	2004	Winfried Auzinger Othmar Koch Ewa Weinmüller
+	Error estimates for solutions of incorrectly posed linear problems	1969	В. К. Иванов T.I. Korolyuk
+	Error estimation for ill-posed problems	2015	A. G. Yagola
+	Corrections to "Error Covariance Analysis of a Karhunen-Loeve Collocation Estimator"	1986
+	An hp-version error estimate of spectral collocation methods for weakly singular Volterra integro-differential equations with vanishing delays	2024	Yu Qin Chengming Huang
+	Bernstein Collocation Method for Solving High-Order Singular Differential–Difference Equations	2023	V. Appalanaidu G. V. S. R. Deekshitulu
+	Asymptotically Accurate Estimates of the Error for Exponentially Convergent Quadratures	2022	V. S. Khokhlachev А. А. Белов

Cited by (34)

Action	Title	Year	Authors
+ PDF Chat	Limit Properties of Solutions of Singular Second-Order Differential Equations	2009	Irena Rachůnková Svatoslav Staněk Ewa Weinmüller Michael Zenz
+ PDF Chat	Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations	2014	Winfried Auzinger Othmar Koch Amir Saboor Bagherzadeh
+ PDF Chat	A unified approach to singular problems arising in the membrane theory	2010	Irena Rachůnková Gernot Pulverer Ewa Weinmüller
+ PDF Chat	Near critical, self-similar, blow-up solutions of the generalised Korteweg–de Vries equation: Asymptotics and computations	2019	Pierluigi Amodio Chris Budd Othmar Koch Vivi Rottschäfer Giuseppina Settanni Ewa Weinmüller
+	Neumann problems with time singularities	2010	Irena Rachůnková Svatoslav Staněk Ewa Weinmüller Michael Zenz
+ PDF Chat	Collocation methods for index 1 DAEs with a singularity of the first kind	2009	Othmar Koch Roswitha März Dirk Praetorius Ewa Weinmüller
+	New a posteriori error estimates for singular boundary value problems	2005	Winfried Auzinger Othmar Koch Dirk Praetorius Ewa Weinmüller
+	Error Estimation Techniques Based on Defect Computation and Global Reconstruction	2010	Winfried Auzinger Theodore E. Simos George Psihoyios Ch. Tsitouras
+	The adapted block boundary value methods for singular initial value problems	2018	Huiru Wang Chengjian Zhang
+	Numerical Treatment of Singular BVPs: The New MATLAB Code bvpsuite	2009	G. Kitzhofer Othmar Koch Ewa Weinmüller Theodore E. Simos George Psihoyios Ch. Tsitouras
+	An Approach to Determining the Number of Time Intervals for Solving Dynamic Optimization Problems	2018	Evgeny Lazutkin Abebe Geletu Pu Li
+	Numerical treatment of singular ODEs using finite difference and collocation methods	2024	Matthias Hohenegger Giuseppina Settanni Ewa Weinmüller Mered Wolde
+	An efficient Sinc-collocation method via the DE transformation for eighth-order boundary value problems	2022	Wenlin Qiu Da Xu Jun Zhou Jing Guo
+	On nonlinear singular BVPs with nonsmooth data. Part 2: Convergence of collocation methods	2021	Felix Karl Auer Winfried Auzinger Jana Burkotová Irena Rachůnková Ewa Weinmüller
+	Numerical Solution of the Density Prole Equation with p-Laplacians	2011	Gottfried Hastermann Pedro M. Lima M. L. Morgado Ewa B. Weinm
+	On a singular boundary value problem arising in the theory of shallow membrane caps	2006	Irena Rachůnková Othmar Koch Gernot Pulverer Ewa Weinmüller
+ PDF Chat	Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics	2007	G. Kitzhofer Othmar Koch Pedro M. Lima Ewa Weinmüller
+ PDF Chat	Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics	2007	G. Kitzhofer Othmar Koch Pedro M. Lima Ewa Weinmüller
+ PDF Chat	Density profile equation with p-Laplacian: Analysis and numerical simulation	2013	Gottfried Hastermann Pedro M. Lima M. Luísa Morgado Ewa Weinmüller
+	p-Laplacian: Analysis and Numerical Simulation	2013	Density Prole Gottfried Hastermann Pedro M. Lima Ewa Weinmüller
+	Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics	2006	G. Kitzhofer Othmar Koch Pedro M. Lima Ewa Weinmüller
+	Analysis and numerical simulation of positive and dead-core solutions of singular two-point boundary value problems	2008	Svatoslav Staněk Gernot Pulverer Ewa Weinmüller
+	A Runge-Kutta BVODE Solver with Global Error and Defect Control	2013	Jason J. Boisvert Paul Muir Raymond J. Spiteri
+	Efficient mesh selection for collocation methods applied to singular BVPs	2004	Winfried Auzinger Othmar Koch Ewa Weinmüller
+ PDF Chat	On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity	2014	Jana Burkotová Irena Rachůnková Svatoslav Staněk Ewa Weinmüller
+	Boundary-Value Problems for Differential-Algebraic Equations: A Survey	2015	René Lamour Roswitha März Ewa Weinmüller
+	On singular BVPs with nonsmooth data: convergence of the collocation schemes	2017	Jana Burkotová Irena Rachůnková Ewa Weinmüller
+	Numerical Solution of singular Eigenvalue Problems for ODEs with a Focus on Problems Posed on Semi-Inflnite Intervals	2010	Robert Hammerling Othmar Koch Christa Simon Ewa B. Weinm
+	On nonlinear singular BVPs with nonsmooth data. Part 1: Analytical results	2018	Jana Burkotová Irena Rachůnková Svatoslav Staněk Ewa Weinmüller Stefan Wurm
+ PDF Chat	Computation of Self-similar Solution Profiles for the Nonlinear Schrödinger Equation	2006	Chris Budd Othmar Koch Ewa Weinmüller
+	Quadratic convergence of approximations by CCC-Schoenberg operators	2016	Tina Bosner Mladen Rogina
+	Convergence of Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point	2010	Alexander Dick Othmar Koch
+ PDF Chat	Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations	2006	Winfried Auzinger Ernst Karner Othmar Koch Ewa Weinmüller
+ PDF Chat	Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point	2012	Alexander Dick Othmar Koch Roswitha März Ewa Weinmüller

Citing (17)

Action	Title	Year	Authors
+	A Collocation Code for Boundary Value Problems in Ordinary Differential Equations	2002	Winfried Auzinger Günter Kneisl Othmar Koch Ewa Weinmüller Ewa Weinmüller
+	The effect of nonlocal interactions on the dynamics of the Ginzburg-Landau equation	1996	Jinqiao Duan Hùng Anh Lý Edriss S. Titi
+	Collocation at Gaussian Points	1973	Carl de Boor Blair Swartz
+	Collocation Methods for Singular Boundary Value Problems	1978	F. R. de Hoog Richard Weiß
+ PDF Chat	Analysis of a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problems	2005	Winfried Auzinger Othmar Koch Ewa Weinmüller
+	Collocation for Singular Boundary Value Problems of Second Order	1986	Ewa Weinmüller
+	On the Boundary Value Problem for Systems of Ordinary Second Order Differential Equations with a Singularity of the First Kind	1984	Ewa Weinmüller
+	Iterated Defect Correction for the Solution of Singular Initial Value Problems	2001	Othmar Koch Ewa Weinmüller
+ PDF Chat	The application of Runge-Kutta schemes to singular initial value problems	1985	Frank de Hoog Richard Weiß
+ PDF Chat	Analysis of Discretization Methods for Ordinary Differential Equations	1974	C. W. Gear Hans J. Stetter
+	<i>Theory of Ordinary Differential Equations</i>	1956	Earl A. Coddington Norman Levinson T. Teichmann
+	Difference Methods for Boundary Value Problems with a Singularity of the First Kind	1976	F. R. de Hoog Richard Weiß
+	None	2003	Winfried Auzinger Günter Kneisl Othmar Koch Ewa Weinmüller
+	Efficient mesh selection for collocation methods applied to singular BVPs	2004	Winfried Auzinger Othmar Koch Ewa Weinmüller
+	None	2002	Winfried Auzinger Othmar Koch Ewa Weinmüller
+	INITIAL VALUE PROBLEMS FOR SYSTEMS OF ORDINARY FIRST AND SECOND ORDER DIFFERENTIAL EQUATIONS WITH A SINGULARITY OF THE FIRST KIND	2001	Othmar Koch Peter W. Kofler Ewa Weinmüller
+	Analysis of Discretization Methods for Ordinary Differential Equations	1973	Hans J. Stetter