Behaviour of the trigonometric interpolation in the solution of an eigenvalue problem by using finite element method

Abstract

Finite element method is an dlicicnl method i,"- 'olving ordinary 11m.! partial differential equations in hoth linear ~nd nonlinear ~"'~~ Ihm arise in difl"relll bWllChc5 of ilpplied sciences ~uch a~ hcallmnsfcr, Iluid now, solid Illcclw.ni~~,quun[lIlll mechanics All kinds of problems stich as in;l"ll and boundary value problems and cigcn ...a.lue problem, arc solved by using finite clement methou. In all these casc~ algebraic polynomial or Lagr~ngc interpolation fundwll is used to apprO>.1I11uteth~ field variable. In our prescot ~(udy we have replaced the LJgwnge inlerpolation I"unctionby the IrigonmTIctl'ic interpolations namely sine and tangel1l interpolation in solving <Ill eigenvalue problem by finite clement method.111C result silow~ (hal ~igenvalues obtnin~d by using sine and tnngenl lIllcrpoialion agree well willllhos~ or Lagrange inlerpolatioll.