Boundary methods for solving elliptic problems with singularities and interfaces
SIAM Journal on Numerical Analysis
Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Boundary approximation methods for solving elliptic problems on unbounded domains
Journal of Computational Physics
Mathematica: a system for doing mathematics by computer (2nd ed.)
Mathematica: a system for doing mathematics by computer (2nd ed.)
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The Trefftz method for the Helmholtz equation with degeneracy
Applied Numerical Mathematics
Effective condition number for the finite element method using local mesh refinements
Applied Numerical Mathematics
On solution uniqueness of elliptic boundary value problems
Journal of Computational and Applied Mathematics
Numerical implementation of the EDEM for modified Helmholtz BVPs on annular domains
Journal of Computational and Applied Mathematics
| Hi-index | 7.30 |
For solving Laplace's eigenvalue problems we propose new algorithms using the Trefftz method (TM) (i.e., the boundary approximation method (BAM)), by means of degeneracy of numerical Helmholtz equations. Since piecewise particular solutions can be fully adopted, the new algorithms benefit high accuracy of eigenvalues and eigenfunctions, low cost in CPU time and computer storage. Also the algorithms can be applied to solve the problems with multiple interfaces and singularities. In this paper, error estimates are derived for the approximate eigenvalues and eigenfunctions obtained. Numerical experiments for smooth and singular solutions are reported in this paper to show significance of the algorithms proposed and to verify the theoretical results made.