Approximating solutions to fractional-order Bagley-Torvik equation via generalized Bessel polynomial on large domains

A highly accurate matrix method for solving a class of strongly nonlinear BVP arising in modeling of human shape corneal

“…Utilizing diverse kinds of polynomials such as Legendre, Chebyshev, Bessel, Chelyshkov, Laguerre, and Vieta-Lucas functions is considered in literature. [14][15][16][17][18][19][20][21][22][23] Combinations of orthogonal functions with quasilinearization method (QLM) have been successfully applied to many important models in physical sciences, see, cf. previous studies.…”

“…It is well known that collocation‐based numerical approximations provide a promising tool to treat various initial and boundary value model problems in science and engineering. Utilizing diverse kinds of polynomials such as Legendre, Chebyshev, Bessel, Chelyshkov, Laguerre, and Vieta‐Lucas functions is considered in literature 14–23 . Combinations of orthogonal functions with quasilinearization method (QLM) have been successfully applied to many important models in physical sciences, see, cf.…”

An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations

“…In recent years, the study of different models with the aid of these polynomials has witnessed a large increase of research due to their simplicity and the ability to provide good results. For the recent applications of the Bessel polynomials, we draw your attention to some recent works we have done in [27][28][29]. The main goal of this research work is to propose a spectral approach based on a combination of novel Bessel bases as well as some appropriate collocation points for an approximate treatment of the SFDEs in (1).…”

“…It can be obviously observed that the coefficients of B m (ξ) are all positive. Contrary to the Bessel functions of the first kind [30], the novel Bessel functions B m (ξ) are the unique solutions of the following differential equation [27][28][29]…”

Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity

“…In recent decades, collocation techniques based on (orthogonal) polynomials have been successfully applied to various areas of physical science and engineering. They have been proven to be efficient, robust, and provide exponential convergence in many application areas, as can be seen in [29][30][31][32][33][34][35]. The main goal of this study was to give an efficient collocation-based polynomial approximation for the solution to the SMDDE (1).…”