Construction of Superconvergent Discretizations with Differential-Difference Invariants

Axford, R.A.

Los Alamos National Laboratory

关键词: Numerical Solution;    Differential Equations;    Finite Difference Method;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Boundary Conditions;   

DOI  :  10.2172/883452
RP-ID  :  LA-14242
RP-ID  :  W-7405-ENG-36
RP-ID  :  883452

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.