Optimal adaptive solution of initial-value problems with unknown singularities

DOI10.1016/j.jco.2008.02.001zbMath1163.65050OpenAlexW1973967922MaRDI QIDQ945916

Paweł Przybyłowicz, Bolesław Kacewicz

Publication date: 19 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.jco.2008.02.001

zbMATH Keywords

error boundsinitial value problemssingularityoptimal algorithmsadaptive grid

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (9)

Efficient solution of IVPs with right-hand sides having discontinuities on an unknown hypersurface ⋮ Optimality of Euler-type algorithms for approximation of stochastic differential equations with discontinuous coefficients ⋮ Optimal solution of a class of non-autonomous initial-value problems with unknown singularities ⋮ Approximation of piecewise Hölder functions from inexact information ⋮ Strong approximation of solutions of stochastic differential equations with time-irregular coefficients via randomized Euler algorithm ⋮ Complexity of the derivative-free solution of systems of IVPs with unknown singularity hypersurface ⋮ Solving systems of IVPs with discontinuous derivatives-numerical experiments ⋮ Optimal adaptive solution of piecewise regular systems of IVPs with unknown switching hypersurface ⋮ Adaptive Itô-Taylor algorithm can optimally approximate the Itô integrals of singular functions

Cites Work

• Unnamed Item
• How to increase the order to get minimal-error algorithms for systems of ODE
• Almost optimal solution of initial-value problems by randomized and quantum algorithms
• A high accuracy method for solving ODEs with discontinuous right-hand side
• Convergence of linear multistep methods for differential equations with discontinuities
• One-step methods of any order for ordinary differential equations with discontinuous right-hand sides
• The complexity of two-point boundary-value problems with piecewise analytic data
• The randomized complexity of initial value problems
• Adaption allows efficient integration of functions with unknown singularities
• Iterated Defect Correction for the Solution of Singular Initial Value Problems
• The power of adaption for approximating functions with singularities
• Solving Ordinary Differential Equations with Discontinuities
• Uniform Approximation of Piecewise r-Smooth and Globally Continuous Functions

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