Spectral Treatment of High-Order Emden–Fowler Equations Based on Modified Chebyshev Polynomials

This paper is devoted to proposing numerical algorithms based on the use of tau and collocation procedures, two widely used spectral approaches for treatment initial high-order linear non-linear equations singular type, especially those Emden–Fowler type. The class modified Chebyshev polynomials third-kind constructed. generalizes polynomials. A new formula that expresses first-order derivative in terms their original established. establishment this essential reducing a certain terminating hypergeometric function type 5F4(1). development our suggested begins with extraction operational matrix from formula. Expansion’s convergence study performed detail. Some illustrative examples Emden–Flower-type different orders are displayed. Our proposed compared some other methods literature. confirms accuracy high efficiency presented algorithms.