Efficient mesh selection for collocation methods applied to singular BVPs

DOI10.1016/j.cam.2004.10.013zbMath1069.65093OpenAlexW2144828711MaRDI QIDQ1779429

Winfried Auzinger, Ewa B. Weinmüller, Othmar Koch

Publication date: 1 June 2005

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.10.013

zbMATH Keywords

Numerical examplesCollocation methodsAdaptive mesh selectionGlobal error estimationSingular BVPs

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Foreign ownership restrictions: a numerical approach, Efficient numerical solution of the density profile equation in hydrodynamics, On a singular boundary value problem arising in the theory of shallow membrane caps, Automatic grid control in adaptive BVP solvers, A unified approach to singular problems arising in the membrane theory, Adaptivity and computational complexity in the numerical solution of ODEs, Numerical solution of singular ODE eigenvalue problems in electronic structure computations, Asymptotically correct error estimation for collocation methods applied to singular boundary value problems, Analysis and numerical simulation of positive and dead-core solutions of singular two-point boundary value problems, Pathfollowing for essentially singular boundary value problems with application to the complex Ginzburg-Landau equation, New a posteriori error estimates for singular boundary value problems

Uses Software

• Matlab
• bvp4c
• Sbvp
• avalanche.f

Cites Work

• Unnamed Item
• Mesh selection for discrete solution of boundary problems in ordinary differential equations
• The defect correction principle and discretization methods
• Singular boundary value problems for ODEs
• A collocation code for singular boundary value problems in ordinary differential equations
• Analytical and numerical treatment of a singular initial value problem in avalanche modeling.
• On the imperfection sensitivity of complete spherical shells
• Efficient collocation schemes for singular boundary value problems
• Asymptotically correct error estimation for collocation methods applied to singular boundary value problems
• The Application of Runge-Kutta Schemes to Singular Initial Value Problems
• Difference Methods for Boundary Value Problems with a Singularity of the First Kind
• Adaptive Mesh Selection Strategies for Solving Boundary Value Problems
• Collocation Methods for Singular Boundary Value Problems
• Existence and stability of singular heteroclinic orbits for the Ginzburg - Landau equation
• Solving Index-1 DAEs in MATLAB and Simulink
• The convergence of shooting methods for singular boundary value problems
• On the Nonunique Equilibrium States and Buckling Mechanism of Spherical Shells
• Analysis of a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problems