On some wavelet solutions of singular differential equations arising in the modeling of chemical and biochemical phenomena

Abstract

This paper is concerned with the Lane–Emden boundary value problems arising in many real-life problems. Here, we discuss two numerical schemes based on Jacobi and Bernoulli wavelets for the solution of the governing equation of electrohydrodynamic flow in a circular cylindrical conduit, nonlinear heat conduction model in the human head, and non-isothermal reaction–diffusion model equations in a spherical catalyst and a spherical biocatalyst. These methods convert each problem into a system of nonlinear algebraic equations, and on solving them by Newton’s method, we get the approximate analytical solution. We also provide the error bounds of our schemes. Furthermore, we also compare our results with the results in the literature. Numerical experiments show the accuracy and reliability of the proposed methods.

Generalized Shifted Airfoil Polynomials of the Second Kind to Solve a Class of Singular Electrohydrodynamic Fluid Model of Fractional Order

“…Additionally, the Haar wavelet solutions was obtained in [18]. Two other wavelet solutions based on the Bernoulli and Jacobi polynomials were obtained in [19]. Ultimately, an efficient and highly accurate numerical approach based on the Chebyshev polynomial of the second kind was examined in [20].…”

A collocation method for time‐fractional diffusion equation on a metric star graph with η$$ \eta $$ edges

“…43 Several other studies are available for solving the differential equations, for example, Haar wavelet, 44 Laguerre wavelet, 45 Hermite wavelet, 46 Gegenbauer wavelet, 47 and Jacobi wavelet. 48 To the best of the author's knowledge, the proposed method is one of the first collocation method in literature that deals with the solution of TFDE on metric star graph using wavelets numerically. Generally, the collocation methods are based on a differential operator approach; that is, the unknown variable is approximated by basis functions and then differentiation of the basis function is calculated to approximate the derivatives.…”

“…More specifically, Islam et al demonstrate Haar wavelet collocation method for boundary value problem for different boundaries, 40 and Raza and Khan utilized Haar wavelet for investigating neutral delay differential equations, 41 while the solution for singularly perturbed differential–difference equation is approximated in Raza et al 42 Mehandiratta et al developed Haar wavelet method for FDEs 43 . Several other studies are available for solving the differential equations, for example, Haar wavelet, 44 Laguerre wavelet, 45 Hermite wavelet, 46 Gegenbauer wavelet, 47 and Jacobi wavelet 48 …”