https://doi.org/10.1140/epjp/i2011-11097-5
Regular Article
Discrete approximations of differential equations via trigonometric interpolation
Department of Mathematics and Computer Science, Concordia College, 901 8th Str. South, Moorhead, MN, USA
* e-mail: obihun@cord.edu
Received:
29
August
2011
Revised:
14
September
2011
Accepted:
17
September
2011
Published online:
19
October
2011
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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2011
