Adaptivity and computational complexity in the numerical solution of ODEs

DOI10.1016/j.jco.2007.11.004zbMath1145.65046OpenAlexW2060306687MaRDI QIDQ933414

Silvana Ilie, Robert M. Corless, Gustaf Söderlind

Publication date: 21 July 2008

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2007.11.004

zbMATH Keywords

numerical examplesboundary value problemserror boundsinitial value problemsinformation-based complexityadaptive numerical methodsHölder meanadaptive step size controlgrid deformation map

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Complexity and performance of numerical algorithms (65Y20) Linear boundary value problems for ordinary differential equations (34B05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (8)

Computational complexity of solving polynomial differential equations over unbounded domains ⋮ Blendstrings: an environment for computing with smooth functions ⋮ Automatic grid control in adaptive BVP solvers ⋮ The impact of smooth \(W\)-grids in the numerical solution of singular perturbation two-point boundary value problems ⋮ Extremely low order time-fractional differential equation and application in combustion process ⋮ Computation and Applications of Mathieu Functions: A Historical Perspective ⋮ Polynomial cost for solving IVP for high-index DAE ⋮ A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection

Uses Software

• COLSYS

Cites Work

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• Adaptive techniques for spline collocation
• Constant coefficient linear multistep methods with step density control
• Thirteen ways to estimate global error
• Efficient mesh selection for collocation methods applied to singular BVPs
• A new view of the computational complexity of IVP for ODE
• On the global error of discretization methods for highly-oscillatory ordinary differential equations
• Global bounds on numerical error for ordinary differential equations
• Time-step selection algorithms: adaptivity, control, and signal processing
• Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time
• Global errors of numerical ODE solvers and Lyapunov's theory of stability
• An optimal control approach to a posteriori error estimation in finite element methods
• Collocation Software for Boundary-Value ODEs
• A Survey of Some Global Methods for Solving Two-Point BVPs
• Collocation for Two-Point Boundary Value Problems Revisited
• Convergence of Adaptive Finite Element Methods
• An elementary solution of a minimax problem arising in algorithms for automatic mesh selection
• Explicit, Time Reversible, Adaptive Step Size Control
• Digital filters in adaptive time-stepping

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