The analysis of flows with free boundaries is a non-linear problem, since their forms are not known in advance and must be found. described method effective for various problems dynamic conditions on boundaries. This iterative based the quasi-linearization boundary velocity potential proposed by A.N. Ivanov 1962. iterations include successive solutions Fredholm integral equations second kind (a...

ABSTRACT. In this paper, a numerical method is constructed for solving one-dimensional time dependent modified Burgers’ equation for various values of Reynolds number. At high Reynolds number, an inviscid boundary layer is produced in the neighborhood of right part of the lateral surface of the domain and the problem can be considered as a non-linear singularly perturbed problem involving a sma...

The radiation and thermal diffusion effects on mixed convection flow of couple stress fluid through a channel are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the Spectral Quasi-linearization Method (QLM). The results, which ar...

This paper provides a technique to investigate the solutions of generalized nonlinear singular Lane–Emden equations of first and second kinds by using a Haar wavelet quasi-linearization approach. The Lane–Emden equation is widely studied and is treated as a challenging equation in the theory of stellar structure for the gravitational potential of a self gravitating, spherically symmetric polytr...

We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...