Stability of difference schemes in the maximum-norm

DOI10.1016/0022-0396(65)90008-2zbMath0259.65086OpenAlexW1965139815MaRDI QIDQ2560044

Vidar Thomée

Publication date: 1965

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(65)90008-2

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

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Cites Work

• Unnamed Item
• Estimates for translation invariant operators in \(L^p\) spaces
• Maximum bounds for the solutions of initial value problems for partial difference equations
• Trigonometric Polynomials and Difference Methods of Maximum Accuracy
• Systems of conservation laws
• Polynomial Approximation of Bernstein Type
• On integration of parabolic equations by difference methods: I. Linear and quasi‐linear equations for the infinite interval
• Symmetric hyperbolic linear differential equations