A priori error estimation in terms of the third derivative for the method of successive approximations applied to ODE's
DOI10.1007/BF02832047zbMath1113.65080MaRDI QIDQ861471
Publication date: 29 January 2007
Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)
initial value problemsa priori error estimateLipschitzian third-order derivativeperturbed trapezoidal quadrature rule
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) Approximate quadratures (41A55) Remainders in approximation formulas (41A80)
Cites Work
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- Special issue: Numerical methods for ordinary differential equations (ANODE 2001), Auckland, New Zealand, January 8--12, 2001. Selected papers
- Numerical methods for ordinary differential equations in the 20th century
- Continuous numerical methods for ODEs with defect control
- Stability of numerical methods for ordinary differential equations
- On a new one-step method for numerical solution of initial-value problems in ordinary differential equations
- Analysis of Error Control Strategies for Continuous Runge–Kutta Methods
- One-Stage Parallel Methods for the Numerical Solution of Ordinary Differential Equations
- Two-Stage Parallel Methods for the Numerical Solution of Ordinary Differential Equations
- Numerical Solution of Ordinary Differential Equations
- Optimal Time Step Control for the Numerical Solution of Ordinary Differential Equations
- Comparing Numerical Methods for Ordinary Differential Equations
- Some applications of continuous Runge-Kutta methods
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