On filter-successive linearization methods for nonlinear semidefinite programming

In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.

MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.

Simultaneous effects of chemical reaction and Ohmic heating with heat and mass transfer over a stretching surface: A numerical study

In this article, we have considered the simultaneous influence of ohmic heating and chemical reaction on heat and mass transfer over a stretching sheet. The effects of applied magnetic field are also taken into consideration while the induced magnetic field is not considered due to very small magnetics Reynolds number. The governing flow problem comprises of momentum, continuity, thermal energy and concentration equation which are transformed into highly nonlinear coupled ordinary differential equations by means of similarity transforms, which are then, solved numerically with the help of Successive Linearization method(SLM) and Chebyshev Spectral collocation method. Numerical values of skin friction coefficient, local Nusselt number, and Sherwood number are also taken into account with the help of tables. The physical influence of the involved parameters of flow velocity, temperature and concentration distribution is discussed and demonstrated graphically. The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.

A SUCCESSIVE LEAST SQUARES METHOD FOR STRUCTURED TOTAL LEAST SQUARES

A new method for Total Least Squares (TLS) problems is presented. It differs from previous approaches and is based on the solution of successive Least Squares problems. The method is quite suitable for Structured TLS (STLS) problems. We study mostly the case of Toeplitz matrices in this paper. The numerical tests illustrate that the method converges to the solution fast for Toeplitz STLS problems. Since the method is designed for general TLS problems, other structured problems can be treated similarly.

Regression analysis and features of negative activation energy for MHD nanofluid flow model:A comparative study

This article elucidates the impact of activation energy on magnetohydrodynamic(MHD)stagnation point nanofluid flow over a slippery surface in a porous regime with thermophoretic and Brownian diffusions.Negative activation energy is scarce in practice,but the impact of negative activation energy could not be neglected as it is noticed in chemical processes.The rate of some Arrhenius-compliant reactions is retarded by increasing the temperature and is therefore associated with negative activation energies,such as exothermic binding of urea or water.In some processes,the temperature dependence of the pressure-induced unfolding and the urea-induced unfolding of proteins at ambient pressure give negative activation energies.The present mathematical model is solved with successive linearization method(a spectral technique).A comparison of results is made for negative and positive values of activation energy.Apart from it,the quadratic multiple regression model is discussed briefly and explained with bar diagrams.It is observed that with rise in unsteadiness parameter from 0 to 1(taking positive activation energy),skin friction and Sherwood number are increased by 9.36%and 19%respectively,and Nusselt number is decreased by 26%.However,for negative activation energy,9.36%and 112%enhancement is observed in skin friction and Sherwood number,respectively.

The effects of cross-diffusion and radiation on mixed convection from a vertical flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation

In this paper,we propose a new application of a recent semi-numericalsuccessive linearization method(SLM)in solving highly coupled,nonlinear boundaryvalue problem.The method is presented in detail by solving the problem of steady flowof mixed convection and an incompressible viscous hydromagnetic fluid from a verticalflat plate embedded in a fluid-saturated porous medium.The governing partial differentialequations are transformed into a system of ordinary differential equations and then solvedby SLM.The effects of different physical parameters on the velocity,temperature,andconcentration profiles are determined and discussed.The skin-friction,and heat and masstransfer coefficients have been obtained and analyzed for various physical parametricvalues.The results are presented numerically through graphs and tables for both assistingand opposing flows to observe the effects of various parameters encountered in the equations.

NONLINEAR RANK-ONE MODIFICATION OF THE SYMMETRIC EIGENVALUE PROBLEM

Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method （SLAM）. The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.