Generic method for solving partial differential equations through the design of problem-specific continuous automata

Nicolas Fressengeas (1) , Hervé Frezza-Buet (2)

1 LMOPS - Laboratoire Matériaux Optiques, Photonique et Systèmes
2 SUPELEC-Campus Metz

This paper presents an original and generic numerical method for solving partial differential equations. A new mathematical and systematic method stemming from the local very nature of any differential problem is proposed: a custom tailored continuous automaton is purposely derived from any given differential problem so that its steady state yields the solution in a quantitatively correct way. The combined use of formal computing and continuous automata thus offers the unique possibility to completely automate the process from formal problem specification to its numerical solution.

Mots clés: Automates Cellulaires; Equations différentielles

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Nicolas Fressengeas, Hervé Frezza-Buet. Generic method for solving partial differential equations through the design of problem-specific continuous automata. 2006. ⟨hal-00107064v3⟩