ON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES

Authors

  • Decio Levi Dip. Math. Phys. Roma Tre University
  • Miguel A. Rodriguez Dept. Fisica Teorica II Facultad de Fisicas Universidad Complutense 28040-Madrid

DOI:

https://doi.org/10.14311/AP.2016.56.0236

Keywords:

partial differential and difference equations, discretization, the Clairaut--Schwarz--Young theorem

Abstract

In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing a partial differential equation on an arbitrary lattice. An open problem is the meaning of a lattice which does not satisfy the Clairaut–Schwarz–Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut–Schwarz–Young theorem. A discussion on the numerical results is presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations.

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Published

2016-06-30

How to Cite

Levi, D., & Rodriguez, M. A. (2016). ON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES. Acta Polytechnica, 56(3), 236–244. https://doi.org/10.14311/AP.2016.56.0236

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Section

Articles