Construction of Superconvergent Discretizations with Differential-Difference Invariants
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.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 883452
- Report Number(s):
- LA-14242
- Country of Publication:
- United States
- Language:
- English
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