Collocation interval finite element method

Based on shortcoming analysis of `point approximation'interval finite element method with Taylor expansion, collocation intervalfinite element method based on the first Chebyshev polynomials which canapproach objective function in global domain is proposed in this paper. Themethod does not require the sensitivities of the objective function withrespect to uncertain variables and the assumption of narrow interval is alsonot needed. The method is suitable for solving the case that the objectivefunction is strongly nonlinear with respect to the uncertain variables. Theorthogonal expansion coefficients of the objective function are obtainedfrom Gauss-Chebyshev quadrature formula. So Gauss integration points arecollocated in the intervals of uncertain variables. The main computationaleffort is to calculate the values of objective function at Gaussianintegration points. When the number of the uncertain variables is $m$ and theten-point Gauss integral method is introduced, it is needed to analyze thesystem with 12m times. Examples show that the collocation interval finiteelement method can still obtain almost exact interval bounds in the casethat other interval finite element methods are invalid.