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From backward approximations to Lagrange polynomials in discrete advection-reaction operators. (English) Zbl 1483.47126

Summary: In this work we introduce a family of operators called discrete advection-reaction operators. These operators are important on their own right and can be used to efficiently analyze the asymptotic behavior of a finite differences discretization of variable coefficient advection-reaction-diffusion partial differential equations. They consist of linear bidimensional discrete dynamical systems defined in the space of real sequences. We calculate explicitly their asymptotic evolution by means of a matrix representation. Finally, we include the special case of matrices with different eigenvalues to show the connection between the operators evolution and interpolation theory.

MSC:

47N40 Applications of operator theory in numerical analysis
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
39A12 Discrete version of topics in analysis
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