Bivariate pseudospectral collocation algorithms for nonlinear partial differential equations.

Doctor of Philosophy in Applied Matheatics. University of KwaZulu-Natal, Pietermaritzburg 2016.Abstract available in PDF file

Overlapping grid spectral collocation methods for nonlinear differential equations modelling fluid flow problems.

Doctoral Degree. University of KwaZulu-Natal, Durban.The focus of this thesis is on computational grid-manipulation to enhance the accuracy, convergence and computational efficiency of spectral collocation methods for the solution of differential equations in fluid mechanics. The need to develop highly accurate, convergent and computationally efficient numerical techniques for solving nonlinear problems is an ever-recurring theme in numerical mathematics. Spectral methods have been shown in the literature to be more accurate and efficient than some common numerical methods, such as finite difference methods. However, their accuracy deteriorates as the computational domain increases and when the number of grid points reaches a certain critical value. The spectral collocation algorithm produces dense matrix equations, for which there is no known efficient solution method. These deficiencies necessitate the development of spectral techniques that produce less dense matrix equations using fewer grid points. This thesis presents a new improvement in spectral collocation methods with particular application to nonlinear differential equations that model problems arising in fluid mechanics. The improvement described in this thesis requires the use of overlapping grids when descritizing the solution domain for Chebyshev spectral collocation method. The thesis is presented in two related subdivisions. In Part A, the overlapping grid approach is used only in space variable when solving nonlinear ordinary and partial differential equations. Subsequently, the overlapping grid approach is used in both the space and time variables in the solution of partial differential equations. This thesis is also devoted to analysing solutions of fluid flow models through various practical geometries with particular interest in non-Newtonian fluid flows. The physics of these fluid flows is studied through parametric studies on the effects of diverse thermophysical parameters on the fluid properties, changes in shear stresses, and heat and mass transport. Key findings, are inter alia, that the overlapping multi-domain spectral techniques are computationally efficient, produce stable and accurate results using a small number of grid points in each subinterval and in the entire computational domain. Using the overlapping grids yields less dense coefficient matrices that invert easily. Changes in thermophysical parameters has significant consequences for the fluid properties, and heat and mass transfer processes

Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis

This thesis is devoted to the development of algorithms for solving nonsmooth nonconvex problems. Some of these algorithms are derivative free methods.Doctor of Philosoph

Aeronautical engineering: A continuing bibliography with indexes (supplement 279)

This bibliography lists 759 reports, articles, and other documents introduced into the NASA scientific and technical information system in May 1992. Subject coverage includes: design, construction, and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Друга міжнародна конференція зі сталого майбутнього: екологічні, технологічні, соціальні та економічні питання (ICSF 2021). Кривий Ріг, Україна, 19-21 травня 2021 року

Second International Conference on Sustainable Futures: Environmental, Technological, Social and Economic Matters (ICSF 2021). Kryvyi Rih, Ukraine, May 19-21, 2021.Друга міжнародна конференція зі сталого майбутнього: екологічні, технологічні, соціальні та економічні питання (ICSF 2021). Кривий Ріг, Україна, 19-21 травня 2021 року