On the relation between elementary partial difference equations and partial differential equations

DOI10.1016/S0168-0072(98)00006-2zbMath0928.03071MaRDI QIDQ1295376

I. P. Van den Berg

Publication date: 9 January 2000

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

zbMATH Keywords

shadownonstandard analysispartial difference equationsheat transfer equationinternal set theorystroboscopy\(S\)-continuous solutions to difference equationsinfinitesimalization of an observed physical scenario

Mathematics Subject Classification ID

Heat equation (35K05) Additive difference equations (39A10) Discrete version of topics in analysis (39A12) Nonstandard models in mathematics (03H05) Physics (00A79) Other applications of nonstandard models (economics, physics, etc.) (03H10)

Related Items (8)

Describing limits of integrable functions as grid functions of nonstandard analysis ⋮ Behavior of some higher order nonlinear rational partial difference equations ⋮ Discretisations of higher order and the theorems of Faà di Bruno and DeMoivre-Laplace ⋮ A grid function formulation of a class of ill-posed parabolic equations ⋮ Grid functions of nonstandard analysis in the theory of distributions and in partial differential equations ⋮ Discrete buckling model for corrugated beam ⋮ Asymptotics of families of solutions of nonlinear difference equations ⋮ Unnamed Item

Cites Work

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• Nonstandard asymptotic analysis
• From discrete to continuous time
• Extended use of IST
• Nonstandard analysis. A practical guide with applications
• Nonstandard analysis in practice
• Survey of the stability of linear finite difference equations
• Nonstandard Measure Theory and its Applications
• "Almost" Implies "Near"
• Applications of nonstandard analysis to partial differential equations—I. the diffusion equation
• Internal set theory: A new approach to nonstandard analysis

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