L255 Andrew C Cullen - Thesis_Redacted.pdf (15.96 MB)

Download file# A novel numerical solver for nonlinear boundary value problems, with applications to the forced Gardner equation

thesis

posted on 2019-04-03, 23:25 authored by ANDREW CRAIG CULLENNonlinear differential equations appear within a wide range of fields, however, solving these problems is particularly difficult. This work charts the development of a suite of new, numerical tools for solving nonlinear differential equations. These tools significantly outperform currently existing methods, in both the amount of time required to solve the problems, and the range of problems that can be approached.
After analysing the properties of these tools, they are applied to the forced Gardner equation. This problem arises in geophysical fluid dynamics, and has particular implications to climate change and extreme weather events.

## History

## Campus location

Australia## Principal supervisor

Simon Rex Clarke## Year of Award

2018## Department, School or Centre

Mathematical Sciences## Course

Doctor of Philosophy## Degree Type

DOCTORATE## Faculty

Faculty of Science## Usage metrics

## Categories

- Geophysical and environmental fluid flows
- Numerical analysis
- Ordinary differential equations, difference equations and dynamical systems
- Applications in physical sciences
- Atmospheric sciences not elsewhere classified
- Applied computing not elsewhere classified
- Theory of computation not elsewhere classified
- Fluid mechanics and thermal engineering not elsewhere classified
- Modelling and simulation
- Applied mathematics not elsewhere classified
- Numerical solution of differential and integral equations
- Numerical and computational mathematics not elsewhere classified
- Computational complexity and computability
- Numerical computation and mathematical software

## Keywords

HomotopyAnalysisMethodHomotopy Analysis MethodGegenbauerUltrasphericalGegenbauer Homotopy Analysis Methodnumericalnonlinearcomputational physicsSpectralHAMGHAMSHAMalgorithmsKorteweg-de VriesKdVfKdVmKdVGardnercomputationoperationscomputational complexityfluidswavesrossbyatmosphericcomplexity analysisGeophysical Fluid DynamicsNumerical AnalysisOrdinary Differential Equations, Difference Equations and Dynamical SystemsComputational PhysicsAtmospheric SciencesApplied Computer ScienceComputation Theory and MathematicsFluidisation and Fluid MechanicsSimulation and ModellingApplied Mathematics not elsewhere classifiedNumerical Solution of Differential and Integral EquationsNumerical and Computational Mathematics not elsewhere classifiedAnalysis of Algorithms and ComplexityNumerical ComputationFluid Physics