PENGGUNAAN INTERPOLASI HERMITE KUBIK DALAM PENYELESAIAN PERSAMAAN STURM-LIOUVILLE DENGAN METODE ELEMEN HINGGA - Maryono, Dwi (Journal of Mathematics and Mathematics Education, 2011)
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 obtainedÂ using finite element methods. The purpose of this research is to obtain the details ofÂ theÂ constructionÂ ofÂ finiteÂ elementÂ methodÂ usingÂ cubicÂ HermiteÂ interpolationÂ inÂ Â Â solvingÂ Sturm-Liouville equations. The result shows that the solutions of the finite element method using cubic Hermite interpolation isÂ goodÂ enoughÂ inÂ solvingÂ SturmÂ LiouvilleÂ equation.Â BasedÂ onÂ theÂ example,Â itsÂ errorÂ dependsÂ onÂ the elementâs length and the index of the eigenvalue or eigen function. Keywords : finite element, Sturm-Liouville, Hermite Interpolation, Eigen value