A surprisingly effective algorithm for the simplification of integrals and sums arising in the partial differential equations and numerical methods

Diogo A Gomes, Mher Safaryan, Ricardo de Lima Ribeiro, Mohammed Sayyari
January 2020
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Abstract

Conservation laws and dissipated quantities are fundamental in analysis. Here we discuss them in partial differential equations and their discretizations. These quantities are integral expressions or, in the discrete case, sums. Often, checking their conservation or dissipation involves tedious computations. Here, we describe a simple algorithm that relies only on linear algebra ideas to simplify these expressions or sums. Also, we discuss another technique to further simplify integral expressions. The, so called, symmetrization that helps to uncover the sign of such integrals. Next, we outline the implementation, including the handling of parametric expressions. Finally, we present some applications to partial differential equations and numerical methods.

Type
Preprint
Publication
In King Abdullah University of Science and Technology
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symbolic computation
Mohammed Sayyari
Mohammed Sayyari
Postdoc & Adjunct

Mohammed is a systems thinker. His Mathematical interests are in Numerical Analysis, HPC, entropy-stable high-order methods, and boundary conditions. His Scientific interests are in the development of robust and efficient numerical methods for fluid flow models relevant to our changing climate.

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