SWhat changed
Makes a specified consistent linear approximation converge for all initial data exactly when its update powers satisfy the uniform finite-horizon stability condition.
Scientific scope
Makes a specified consistent linear approximation converge for all initial data exactly when its update powers satisfy the uniform finite-horizon stability condition. Exact target is 1956 Part I, not the entire 27 page survey. The theorem assumes a complete normed linear space, properly posed linear evolution with a dense unique genuine-solution class and bounded solution extension, bounded whole-space linear updates, a specified joint spatial/time mesh path and consistency uniform in time on a dense genuine-solution class. Convergence is for every initial element as the mesh refines with n*dt tending to a finite time in[0, T]. Stability bounds update powers uniformly over the family/horizon; it is not merely a one-step norm<=1 or eigenvalue test. A specially chosen datum can converge in an unstable scheme without satisfying the all-data statement. The original assumes exact arithmetic and fixed finite horizon, not arbitrary long-time/roundoff guarantees. Part II introduction gives restricted Fourier cases and extra hypotheses for spectral sufficiency; its detailed 277–292 proofs/examples are unread and excluded. Part I 267–275 and bibliography 293 prose/source proof read, formula glyphs imperfect; no independent proof or implementation certification. Nonlinear, adaptive/nonhomogeneous-boundary extensions require their own assumptions.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- P. D. Lax · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- R. D. Richtmyer · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Lax and Richtmyer, Survey of the Stability of Linear Finite Difference Equations (1956): Part I equivalence theorem
- Wiley:1956 Lax–Richtmyer survey metadata and references
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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