Trotter products and reaction-diffusion equations

  • Authors:

  • Emil Popescu

  • Affiliations:

  • Department of Mathematics and Computer Science, Technical University of Civil Engineering, Bd. Lacul Tei 124, 38RO-020396 Bucharest, Romania

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

In this paper, we study a class of generalized diffusion-reaction equations of the form @?u@?t(x,t)=(Au(@?,t))(x)+f(x,u(x,t)), where A is a pseudodifferential operator which generates a Feller semigroup. Using the Trotter product formula we give a corresponding discrete time integro-difference equation for numerical solutions.