A new compact finite difference quasilinearization method for nonlinear evolution partial differential equations

P.G. Dlamini, and M. Khumalo. "A new compact finite difference quasilinearization method for nonlinear evolution partial differential equations." Open Mathematics 15.1 (2017): 1450-1462. <http://eudml.org/doc/288535>.

@article{P2017,
abstract = {This article presents a new method of solving partial differential equations. The method is an improvement of the previously reported compact finite difference quasilinearization method (CFDQLM) which is a combination of compact finite difference schemes and quasilinearization techniques. Previous applications of compact finite difference (FD) schemes when solving parabolic partial differential equations has been solely on discretizing the spatial variables and another numerical technique used to discretize temporal variables. In this work we attempt, for the first time, to use the compact FD schemes in both space and time. This ensures that the rich benefits of the compact FD schemes are carried over to the time variable as well, which improves the overall accuracy of the method. The proposed method is tested on four nonlinear evolution equations. The method produced highly accurate results which are portrayed in tables and graphs.},
author = {P.G. Dlamini, M. Khumalo},
journal = {Open Mathematics},
keywords = {Compact finite differences; Quasilinearization; Nonlinear evolution equations},
language = {eng},
number = {1},
pages = {1450-1462},
title = {A new compact finite difference quasilinearization method for nonlinear evolution partial differential equations},
url = {http://eudml.org/doc/288535},
volume = {15},
year = {2017},
}

TY - JOUR
AU - P.G. Dlamini
AU - M. Khumalo
TI - A new compact finite difference quasilinearization method for nonlinear evolution partial differential equations
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1450
EP - 1462
AB - This article presents a new method of solving partial differential equations. The method is an improvement of the previously reported compact finite difference quasilinearization method (CFDQLM) which is a combination of compact finite difference schemes and quasilinearization techniques. Previous applications of compact finite difference (FD) schemes when solving parabolic partial differential equations has been solely on discretizing the spatial variables and another numerical technique used to discretize temporal variables. In this work we attempt, for the first time, to use the compact FD schemes in both space and time. This ensures that the rich benefits of the compact FD schemes are carried over to the time variable as well, which improves the overall accuracy of the method. The proposed method is tested on four nonlinear evolution equations. The method produced highly accurate results which are portrayed in tables and graphs.
LA - eng
KW - Compact finite differences; Quasilinearization; Nonlinear evolution equations
UR - http://eudml.org/doc/288535
ER -