Abstract
Systems of coupled non-linear differential equations arise in science and engineering are inherently nonlinear and difficult to find exact solutions. However, in the late nineties, Liao introduced Optimal Homotopy Analysis Method (OHAM), and it allows us to construct accurate approximations to the systems of coupled nonlinear differential equations. The drawback of OHAM is, we must first choose the proper auxiliary linear operator and then solve the linear higher-order deformation equation by spending lots of CPU time. However, in the latest innovation of Liao's "Method of Directly Defining inverse Mapping (MDDiM)" which he introduced to solve a single nonlinear ordinary differential equation has great freedom to define the inverse linear map directly. In this way, one can solve higher order deformation equations quickly, and it is unnecessary to calculate an inverse linear operator. Our primary goal is to extend MDDiM to solve systems of coupled nonlinear ordinary differential equations. In the first chapter, we will introduce MDDiM and briefly discuss the advantages of MDDiM Over OHAM. In the second chapter, we will study a nonlinear coupled system using OHAM. Next three chapters, we will apply MDDiM to coupled non-linear systems arise in mechanical engineering to study fluid flow and heat transfer. In chapter six we will apply this novel method to study coupled non-linear systems in epidemiology to investigate how diseases spread throughout time. In the last chapter, we will discuss our conclusions and will propose some future work. Another main focus is to compare MDDiM with OHAM.
Notes
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Graduation Date
2019
Semester
Summer
Advisor
Vajravelu, Kuppalapalle
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematics
Format
application/pdf
Identifier
CFE0007624
URL
http://purl.fcla.edu/fcla/etd/CFE0007624
Language
English
Release Date
August 2019
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
STARS Citation
Dewasurendra, Mangalagama, "Semi-Analytical Solutions of Non-linear Differential Equations Arising in Science and Engineering" (2019). Electronic Theses and Dissertations. 6476.
https://stars.library.ucf.edu/etd/6476