On a new quasi-linearization method for systems of nonlinear boundary value problems

Abstract

Communicated by J. BanasiakWe propose a new quasi-linearization technique for solving systems of nonlinear equations. The method finds recursive formulae for higher order deformation equations which are then solved using the Chebyshev spectral collocation method. The implementation of the method is demonstrated by solving the coupled nonlinear equations that govern the injection of a non-Newtonian fluid through the sides of a vertical channel. The equations are also solved numerically and comparison made with the results in the literature. The linearization method is found to be computationally efficient and accurate with a rapidly convergent series solution.

On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects

“…The SQLM has been used in a limited number of studies to solve boundary layer flow, heat and mass transfer problems (see [30]). A comparison with previously published results is shown in Table 1 parameter and Soret parameter, respectively, moreover, the equation of mass is not considered).…”

A new piecewise-quasilinearization method for solving chaotic systems of initial value problems

“…For convenience of the interested reader, we will first present a brief description of the basic idea behind the successive linearization method [18,21,22]. This will be followed by a description of the multi-step extension of the SLM algorithm which is suitable for solving initial value problems with chaotic behaviour.…”

“…The Chebyshev pseudospectral method (or any other collocation method or numerical scheme) is then used to transform the iterative sequence of linearized differential equations into a system of linear algebraic equations which are converted into a matrix system. The method has been successfully applied to a wide variety of scientific models [6,18,[21][22][23]27] over finite and semi-infinite intervals. In the above cited applications the SLM method was applied to boundary value problems which possess smooth solutions.…”

Cross-Diffusion, Viscous Dissipation and Radiation Effects on an Exponentially Stretching Surface in Porous Media

“…The successive linearisation method (SLM) which has been used in a limited number of studies (see [3,5,[20][21][22]32]) is used to solve the governing coupled non-linear system of equations. Recent studies such as [4,22,23] have suggested that the successive linearisation method is accurate and converges rapidly to the numerical results when compared to other semi-analytical methods such as the Adomian decomposition method, the variational iteration method and the homotopy perturbation method. The SLM method can be used in place of traditional numerical methods such as finite differences, Runge-Kutta shooting methods, finite elements in solving non-linear boundary value problems.…”