Generalized Bessel Quasilinearization Technique Applied to Bratu and Lane–Emden-Type Equations of Arbitrary Order

The ultimate goal of this study is to develop a numerically effective approximation technique acquire numerical solutions the integer and fractional-order Bratu singular Lane–Emden-type problems especially with exponential nonlinearity. Both initial boundary conditions were considered fractional derivative being in Liouville–Caputo sense. In direct approach, generalized Bessel matrix method based on collocation points was utilized convert model into nonlinear fundamental equation. Then, quasilinearization employed tackle nonlinearity that arose our problems. Consequently, transform original sequence linear equations, while scheme solve resulting equations iteratively. particular, Neumann or condition form, fast algorithm for computing basis functions presented. error analysis quasilinear approach also discussed. effectiveness present linearized illustrated through several simulations some test examples. Comparisons existing well-known schemes revealed presented an easy-to-implement very convenient Lane–Emden equations.