Solving a class of local and nonlocal elliptic boundary value problems arising in heat transfer

Abstract

This paper deals with a class of Bratu's type, Troesch's, and nonlocal elliptic boundary value problems arising in the heat transfer process. Due to the strong nonlinearity and presence of parameter δ, it is very difficult to solve these problems analytically as well as numerically. By using the Jacobi spectral collocation method, these problems are solved fruitfully. We have shown the numerical as well as theoretical convergence of the suggested scheme. Numerical results are presented through figures and tables, demonstrating the accuracy of the scheme. Results are compared with some known methods to highlight its neglectable error.

A Generalized Diffusion Equation: Solutions and Anomalous Diffusion

“…These operators may be related to different scenarios in connection with anomalous diffusion, which implies memory effects, longrange correlation, and fractal structures, among others. In particular, these fractional operators have been used in many contexts such as boundary value problems [30,31], electric circuits [32,33], and electrical impedance [34,35] (see also Refs. [36][37][38]).…”

Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods

“…An optimal iterative method based on Green's functions and an optimal homotopy analysis method (GF-OHAM) has been studied in [10] and [11] . Finally, the Jacobi spectral method has been proposed recently in [12] to solve two models (I) and (II).…”

“…Direct application of the spectral clique technique is accomplished in the first approach. Unlike the Jacobi spectral method [12] , we describe a spectral algorithm in detail and in particular the convergence of the clique basis functions is established. The main advantage of this technique is that accurate approximate solutions are achieved using a few terms of the truncated series expansions.…”