Effect of hyperbolic interpolation in the finite element solution of an eigenvalue problem

Abstract

Finite element method is an efficient method for solving ordinary and partial differential equations in both lincar and nonlinear cases that arise in different branches of applied sciences slIeh <ISheat transfer, fluid flow, solid meehm:tics, quantum mechanics, All kinds of problems such as initial and boundary value problems and eigenvalue problems are solved by using finite clement method. In all these cases algebraic polynomial or Lagrange interpolation fnnClion is used to approximate the field vari<lble. In our present study we have replaced the Lagrange interpolation function by the Hypcrbolic interpolations namely sine and tangent hyperbolic interpol<ltion in solving an eigenvalue problem by finite element method. The resnlt shows tbat eigenvalucs obtained by using sine and tangcnt hyperbolic interpolation agree well with those of Lagrange interpolatioll.