English

Discrete approximations of differential equations via trigonometric interpolation

Numerical Analysis 2011-08-30 v1 Mathematical Physics math.MP

Abstract

To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the differential operator associated with the equation. We compute the ranks of the matrix representations of a certain class of linear differential operators. Our numerical tests show high accuracy and fast convergence of the method applied to several boundary and eigenvalue problems.

Keywords

Cite

@article{arxiv.1108.5714,
  title  = {Discrete approximations of differential equations via trigonometric interpolation},
  author = {Oksana Bihun and Austin Bren and Michael Dyrud and Kristin Heysse},
  journal= {arXiv preprint arXiv:1108.5714},
  year   = {2011}
}