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Solving uncertain differential equations using interval legendre polynomials based collocation method

Abstract This paper proposes a new technique based on interval Legendre polynomials in the collocation method for solving n-the order uncertain boundary value problems. Firstly, the proposed method is illustrated by different example problems. Further, the developed technique has been used to solve the steady state radon diffusion-advection equation with uncertain (interval) boundary conditions. The results obtained by the proposed method are compared with their exact solutions (in crisp case) in order to demonstrate the validity and applicability of the method.