On the randomized solution of initial value problems

DOI10.1016/j.jco.2010.07.002zbMath1225.65071OpenAlexW1972156125MaRDI QIDQ544122

Thomas Daun

Publication date: 14 June 2011

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

Full work available at URL: https://doi.org/10.1016/j.jco.2010.07.002

zbMATH Keywords

complexitycomparison of methodssystemsnumerical resultsMonte-Carlo algorithminitial value problemRunge-Kutta methodrandomized algorithmEuler method

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Complexity and performance of numerical algorithms (65Y20)

Related Items (21)

Randomized and quantum complexity of nonlinear two-point BVPs ⋮ Adaptive mesh selection asymptotically guarantees a prescribed local error for systems of initial value problems ⋮ Efficient finite-dimensional solution of initial value problems in infinite-dimensional Banach spaces ⋮ Complexity of certain nonlinear two-point BVPs with Neumann boundary conditions ⋮ Efficient solution of IVPs with right-hand sides having discontinuities on an unknown hypersurface ⋮ Convergence in Total Variation of the Euler--Maruyama Scheme Applied to Diffusion Processes with Measurable Drift Coefficient and Additive Noise ⋮ Existence, uniqueness and approximation of solutions to Carathéodory delay differential equations ⋮ A note on the probabilistic stability of randomized Taylor schemes ⋮ Error analysis of randomized Runge-Kutta methods for differential equations with time-irregular coefficients ⋮ On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes ⋮ On the Complexity of Parametric ODEs and Related Problems ⋮ Complexity of the derivative-free solution of systems of IVPs with unknown singularity hypersurface ⋮ Complexity of parametric initial value problems for systems of odes ⋮ Solving systems of IVPs with discontinuous derivatives-numerical experiments ⋮ Optimal global approximation of SDEs with time-irregular coefficients in asymptotic setting ⋮ Truncated Milstein method for non-autonomous stochastic differential equations and its modification ⋮ Complexity of parametric initial value problems in Banach spaces ⋮ On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients ⋮ Randomized Runge-Kutta method -- stability and convergence under inexact information ⋮ On the randomized Euler schemes for ODEs under inexact information ⋮ On the optimal robust solution of IVPs with noisy information

Cites Work

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• 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
• Deterministic and stochastic error bounds in numerical analysis
• The randomized complexity of initial value problems
• Monte Carlo approximation of weakly singular integral operators
• The randomized information complexity of elliptic PDE
• Complexity of initial-value problems for ordinary differential equations of order \(k\)

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