A comparison study of Chebyshev spectral collocation based methods for solving nonlinear second order evolution equations.
Loading...
Date
2015
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
In this study Spectral Quasilinearisation Method (SQLM) coupled with finite differ-
ence and Bivariate Spectral Quasilinearisation Method (BSQLM) in solving second
order nonlinear evolution partial differential equations are compared. Both meth-
ods use Newton-Raphson quasilinearisation method (QLM) and Chebyshev spectral
collocation based on Lagrange interpolation to solve the governing equations. The
Spectral Quasilinearisation Method coupled with finite difference is obtained by ap-
plying the spectral collocation method on space derivatives and finite difference of
time derivatives while the BSQLM is a Bivariate Lagrange interpolation based scheme
in which the spectral collocation method is applied independently to both time and
space derivatives. The applicability of these methods is shown by solving a class
of second order nonlinear evolution partial differential equations (NPDEs), namely
Burgers equation, Burgers-Fisher, Fisher's equation, Newell-Whitehead-Segel equa-
tion and Zeldovich equation that arise in some fields of science and engineering. The
numerical approximation results are validated for accuracy by comparing them with
exact solutions. Tables for Explicit, Implicit and Crank-Nicolson SQLM and BSQLM
with their computational times were generated for comparison; the order of accuracy
for each method and error graphs are presented.
Description
Master of Science in Applied Mathematics. University of KwaZulu-Natal, Pietermaritzburg 2015.
Keywords
Chebyshev systems., Spectral sequences (Mathematics), Collocation methods., Evolution equations, Nonlinear., Theses -- Applied mathematics.