Particle-without-Particle: A Practical Pseudospectral Collocation Method for Linear Partial Differential Equations with Distributional Sources

Author:

Oltean MariusORCID,Sopuerta Carlos F.,Spallicci Alessandro D. A. M.

Funder

Natural Sciences and Engineering Research Council of Canada

LISA France-CNES

Ministerio de Economía y Competitividad

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference76 articles.

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2. Schwartz, L.: Sur l’impossibilité de la Multiplication des Distributions. C. R. Acad. Sci. Paris, 29, 847 (1954). http://sites.mathdoc.fr/OCLS/pdf/OCLS_1954__21__1_0.pdf

3. Li, C.K.: A review on the products of distributions. In: Taş, K., Tenreiro Machado, J.A., Baleanu, D. (eds.) Mathematical Methods in Engineering, pp. 71–96. Springer, Dordrecht (2007). https://link.springer.com/chapter/10.1007/978-1-4020-5678-9_5

4. Colombeau, J.F.: Nonlinear generalized functions: their origin, some developments and recent advances. São Paulo J. Math. Sci. 7, 201 (2013). arXiv:1401.4755

5. Bottazzi, E.: Grid functions of nonstandard analysis in the theory of distributions and in partial differential equations, arXiv:1704.00470 [math] (2017)

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