There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

Basic Ideas.- Systematic Descriptions.- Advanced Approaches.- Convergent Series For Divergent Taylor Series.- Nonlinear Initial Value Problems.- Nonlinear Eigenvalue Problems.- Nonlinear Problems In Heat Transfer.- Nonlinear Problems With Free Or Moving Boundary.- Steady-State Similarity Boundary-Layer Flows.- Unsteady Similarity Boundary-Layer Flows.- Non-Similarity Boundary-Layer Flows.- Applications In Numerical Methods.

Homotopy Analysis Method in Nonlinear Differential Equations

Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

Boundary value problems

Combined impact of Cattaneo-Christov double diffusion and radiative heat flux on bio-convective flow of Maxwell liquid configured by a stretched nano-material surface

A new spectral-homotopy analysis method for the MHD Jeffery-Hamel problem

Numerical solution of binary chemical reaction on stagnation point flow of Casson fluid over a stretching/shrinking sheet with thermal radiation

In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.

/pdf/heat-and-mass-transfer-in-unsteady-rotating-fluid-flow-with-3dl6a0m6qo.pdf

Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy.

A new spectral-homotopy analysis method for solving a nonlinear second order BVP

Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.

/pdf/spectral-relaxation-method-and-spectral-quasilinearization-2jbregnzl8.pdf

Sandile S. Motsa

Papers

A new spectral-homotopy analysis method for the MHD Jeffery-Hamel problem

Numerical solution of binary chemical reaction on stagnation point flow of Casson fluid over a stretching/shrinking sheet with thermal radiation

Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy.

A new spectral-homotopy analysis method for solving a nonlinear second order BVP

Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems