Ultraspherical Differentiation Method for Solving System of Initial Value Differential Algebraic Equations

Abstract In this paper, we introduce a new spectral method based on ultraspherical polynomials for solving systems of initial value differential algebraic equations. Moreover, the suggested method is applicable for a wide range of differential equations. The method is based on a new investigation of the ultraspherical spectral differentiation matrix to approximate the differential expressions in equations. The produced equations lead to algebraic systems and are converted to nonlinear programming. Numerical examples illustrate the robustness, accuracy, and efficiency of the proposed method.

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