Discrete approximations of differential equations via trigonometric interpolation

Details Discrete approximations of differential equations via trigonometric interpolation Discrete approximations of differential equations via trigonometric interpolation

2011-08-29

arxiv.org/abs/1108.5714v1

Mathematics

Numerical Analysis

Scientific paper

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.

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