Convergence of numerical schemes involving powers of the Dirac delta function

DOI10.1016/0022-247X(90)90439-MzbMath0691.65067MaRDI QIDQ582827

M. Adamczewski, J. François Colombeau, Alain-Yves Le Roux

Publication date: 1990

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

stabilityconvergenceshock wavesDirac delta functionsHull elastoplastic methodnonlinear theory of distributions

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Shock waves and blast waves in fluid mechanics (76L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (7)

Intrinsic definition of the Colombeau algebra of generalized functions ⋮ On powers of the compositions involving Dirac-delta and infinitely differentiable functions ⋮ Conservation laws with discontinuous coefficients ⋮ Multiplication of distributions ⋮ Generalized solutions to partial differential equations of evolution type ⋮ Singularities in space-time foam algebras ⋮ The Colombeau generalized nonlinear analysis and the Schwartz linear distribution theory

Cites Work

• Unnamed Item
• Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations
• Holomorphic generalized functions
• Generalized solutions to nonlinear first-order systems
• Borel's theorem for generalized functions
• Multiplications of distributions in elasticity and hydrodynamics

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