On the concepts of convergence, consistency, and stability in connection with some numerical methods

DOI10.1007/BF01406967zbMath0278.65072MaRDI QIDQ1394099

Aarne H. Sipilä, Olavi Nevanlinna, Matti Mäkelä

Publication date: 1974

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132269

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical analysis in abstract spaces (65J99)

Related Items (3)

Two-step numerical methods for parabolic differential equations ⋮ On the convergence of multistep methods for the Cauchy problem for ordinary differential equations ⋮ The simulation of random processes on digital computers: Unavoidable order

Cites Work

• Numerical methods and existence theorems for ordinary differential equations
• Convergence and stability of step-by-step methods for the numerical solution of initial-value problems
• Stabilization of optimal difference operators
• Numerical solution of ordinary differential equations
• On the Convergence of Numerical Solutions to Ordinary Differential Equations
• Block Implicit One-Step Methods
• Linear Multistep Methods with Mildly Varying Coefficients
• Multistep Methods with Variable Matrix Coefficients
• A General Theory of Convergence for Numerical Methods
• Marginal Stability and Stabilization in the Numerical Integration of Ordinary Differential Equations
• A -Stable Composite Multistep Methods
• On the structure of error estimates for finite-difference methods
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