Computationally efficient technique for weight functions and effect of orthogonal polynomials on the average

The properties of orthogonal collocation on finite elements with respect to the choice of orthogonal polynomials are studied. A simplified algorithm for the calculation of the collocation points, weight functions and discretization matrices for first and second order derivatives is presented in terms of the Lagrangian interpolation polynomial. The effect of Legendre and Chebyshev polynomials on the average value of the dependent variable is checked. It is found that the Legendre polynomial gives the better results at the centre and on the average as compare to the Chebyshev polynomial.