Construction of Superconvergent Discretizations with Differential-Difference Invariants | Zendy

R.A. Axford | Zendy

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Construction of Superconvergent Discretizations with Differential-Difference Invariants

Author(s) -

R.A. Axford

Publication year - 2005

Publication title -

osti oai (u.s. department of energy office of scientific and technical information)

Language(s) - English

Resource type - Reports

DOI - 10.2172/883452

Subject(s) - superconvergence , mathematics , eigenvalues and eigenvectors , discretization , boundary value problem , mathematical analysis , differential equation , dirichlet boundary condition , differential (mechanical device) , symmetry (geometry) , finite element method , geometry , physics , thermodynamics , quantum mechanics

To incorporate symmetry properties of second-order differential equations into finite difference equations, the concept of differential-difference invariants is introduced. This concept is applied to discretizing homogeneous eigenvalue problems and inhomogeneous two-point boundary value problems with various combinations of Dirichlet, Neumann, and Robin boundary conditions. It is demonstrated that discretizations constructed with differential-difference invariants yield exact results for eigenvalue spectra and superconvergent results for numerical solutions of differential equations

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