On the numerical solution of the Lane-Emden, Bratu and Troesch equations.
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Date
2020
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Abstract
Many engineering and physics problems are modelled using differential equations, which
may be highly nonlinear and difficult to solve analytically. Numerical techniques are often
used to obtain approximate solutions. In this study, we consider the solution of three nonlinear
ordinary differential equations; namely, the initial value Lane-Emden equation, the
boundary value Bratu equation, and the boundary value Troesch problem. For the Lane-
Emden equation, a comparison is made between the accuracy of solutions using the finite
difference method and the multi-domain spectral quasilinearization method along with
the exact solution. We found that the multi-domain spectral quasilinearization method
gave a better solution. For the Bratu problem, a comparison is made between the spectral
quasilinearization method and the higher-order spectral quasilinearization method. The
higher-order spectral quasilinearization method gave more accurate results. The Troesch
problem is solved using the higher-order spectral quasilinearization method and the finite
difference method. The solutions obtained are compared in terms of accuracy. Overall,
the higher-order spectral quasilinearization method and multi-domain spectral quasilinearization
method gave the accurate solutions, making these two methods to be the most
reliable for these three problems.
Description
Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.