PENGGUNAAN INTERPOLASI HERMITE KUBIK DALAM PENYELESAIAN PERSAMAAN STURM-LIOUVILLE DENGAN METODE ELEMEN HINGGA

Abstract

ABSTRACT: Eigenvalue problems especially Sturm-Liouville equations often occur in physics. Homogenous Dirichlet or mixed boundary value problems can be constructed from these equations. The nontrivial solution from these equations can be obtained  using finite element methods. The purpose of this research is to obtain the details of  the  construction  of  finite  element  method  using  cubic  Hermite  interpolation  in    solving  Sturm-Liouville equations. The result shows that the solutions of the finite element method using cubic Hermite interpolation is  good  enough  in  solving  Sturm  Liouville  equation.  Based  on  the  example,  its  error  depends  on  the element’s length and the index of the eigenvalue or eigen function.

Keywords : finite element, Sturm-Liouville, Hermite Interpolation, Eigen value