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This is basically a review of the Mathematical modeling which is a common practice now a days in industry. A Literature is also given here which comprise of linearity, non linearity and overview of techniques given by various authors along with their solution techniques.An efficient technique is also given which reduce computational time.The technique can be used for various models linear as well as non linear. The technique is simulated with industrial parameters too.

This is basically a review of the technique of orthogonal collocation on finite elements (OCFE) method which is used to solve not only linear differential equations but is quite useful for the solution of non linear equations as well. First of all an introduction of orthogonal polynomials like Jacobi, Legendre and Chebyshev polynomial is presented. Then orthogonal collocation method is discussed for symmetric and non symmetric problems. Technique to form discretization matrices, selection of collocation points and quadrature weights is presented. The method of orthogonal collocation on finite...