To construct basis functions in W 2 ( 1 , 0 ) space to finite element method for 1D two-point boundary-value problems

This paper uses the Ritz method to find approximate solutions to boundary-value problems for ordinary differential equations. We present the approximate finite element solution by a linear combination of the basis functions. Here we get co-efficients of the optimal interpolation formula in W 2 ( 1 , 0 ) space as basis functions. The difference obtained in numerical results and exact solutions illustrates graphically.