Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane–Emden type

• A new second kind Chebyshev (S2KC) operational matrix of derivatives is constructed.
• Numerical solutions of a class of linear and nonlinear Lane–Emden type singular IVPs are obtained.
• The differential equation with its initial conditions is reduced to a system of algebraic equations.

In this paper, we present a new second kind Chebyshev (S2KC) operational matrix of derivatives. With the aid of S2KC, an algorithm is described to obtain numerical solutions of a class of linear and nonlinear Lane–Emden type singular initial value problems (IVPs). The idea of obtaining such solutions is essentially based on reducing the differential equation with its initial conditions to a system of algebraic equations. Two illustrative examples concern relevant physical problems (the Lane–Emden equations of the first and second kind) are discussed to demonstrate the validity and applicability of the suggested algorithm. Numerical results obtained are comparing favorably with the analytical known solutions.