A novel numerical solver for nonlinear boundary value problems, with applications to the forced Gardner equation ANDREW CRAIG CULLEN 10.26180/5bbfcc9710d6c https://bridges.monash.edu/articles/thesis/A_novel_numerical_solver_for_nonlinear_boundary_value_problems_with_applications_to_the_forced_Gardner_equation/7199753 Nonlinear 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. 2019-04-03 23:25:01 Homotopy Analysis Method Homotopy Analysis Method Gegenbauer Ultraspherical Gegenbauer Homotopy Analysis Method numerical nonlinear computational physics Spectral HAM GHAM SHAM algorithms Korteweg-de Vries KdV fKdV mKdV Gardner computation operations computational complexity fluids waves rossby atmospheric complexity analysis Geophysical Fluid Dynamics Numerical Analysis Ordinary Differential Equations, Difference Equations and Dynamical Systems Computational Physics Atmospheric Sciences Applied Computer Science Computation Theory and Mathematics Fluidisation and Fluid Mechanics Simulation and Modelling Applied Mathematics not elsewhere classified Numerical Solution of Differential and Integral Equations Numerical and Computational Mathematics not elsewhere classified Analysis of Algorithms and Complexity Numerical Computation Fluid Physics