Efficient spectral ultraspherical-Galerkin algorithms for the direct solution of 2nth-order linear differential equations

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A Jacobi–Gauss collocation method for solving nonlinear Lane–Emden type equations (2012, methodology): “In the present paper we intend to extend the application of Jacobi polynomials from Galerkin method for solving two-point linear problems (see [6,13,16]) to collocation method to solve nonlinear second-order initial value problems.”
Efficient spectral-Petrov-Galerkin methods for third- and fifth-order differential equations using general parameters generalized Jacobi polynomials (2013, methodology): “[9], have constructed efficient spectral-Galerkin algorithms using compact combinations of orthogonal polynomials for solving elliptic equations of second-order, fourth-order, 2nth-order and (2n+1)th-order in various situations.”