Discrete approximations of differential equations via trigonometric   interpolation
  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. 
Oksana Bihun, Austin Bren, Michael Dyrud, Kristin Heysse
math.NA math-ph math.MP