Multiplicity results by shooting reproducing kernel Hilbert space method for the catalytic reaction in a flat particle

Abstract

In this paper, a model of simultaneous mass and heat transfer within a porous catalyst in a flat particle is considered. A new modification of the shooting reproducing kernel Hilbert space (SRKHS) method is proposed, which is also capable of handling the system of nonlinear boundary value problems by employing Newtons method. The proposed method is a well-performance technique in both predicting and calculating multiple solutions of the nonlinear boundary value problems. Applying the SRKHS method shows that the mentioned model might admit multiple stationary solutions (unique, dual or triple solutions) depending on the values of the parameters of the model. Furthermore, the convergence of the method is proved and some numerical tests reveal the high efficiency of this new version of SRKHS method.

A Novel Method for Solutions of Fourth-Order Fractional Boundary Value Problems

“…Azarnavid et al [17] have investigated the Picard-reproducing kernel Hilbert space method for solving generalized singular nonlinear Lane-Emden type equations. Azarnavid et al [18] have found multiplicity results by shooting reproducing kernel Hilbert space method for the catalytic reaction in a flat particle. Azarnavid et al [19] have used an iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition.…”

Reproducing kernel Hilbert space method based on reproducing kernel functions for investigating boundary layer flow of a Powell–Eyring non-Newtonian fluid

“…The main goal of this work is to apply the reproducing kernel method (RKM) using reproducing kernel functions for investigating the nonlinear differential equation of the Powell-Eyring problem, in an unbounded domain. This method has been applied to many problems successfully [14][15][16][17][18].…”

Reproducing kernel pseudospectral method for the numerical investigation of nonlinear multi-point boundary value problems

“…Recently, several techniques based on the reproducing kernel Hilbert spaces have attracted great attention and are extensively used for the numerical solving of the various types of ordinary and partial differential equations (Abbasbandy and Azarnavid 2016; Azarnavid et al 2015Azarnavid et al , 2018aEmamjome et al 2017;Arqub 2016aArqub , b, 2017aArqub et al 2013Arqub et al , 2016Arqub et al , 2017Al-Smadi et al 2016;Niu et al 2012aNiu et al , b, 2018Lin et al 2012;Akgül and Baleanu 2017;Akgül and Karatas 2015;Akgül et al 2015Akgül et al , 2017Inc et al 2012Inc et al , 2013aSakar et al 2017;Inc and Akgül 2014;Akgül 2015). This paper presents an iterative approach based on reproducing kernel Hilbert space pseudospectral method to find the numerical solution of nonlinear boundary value problems with multi-point boundary conditions.…”