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