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

• Autorzy: P.G. Dlamini , M. Khumalo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Compact finite differences; Quasilinearization; Nonlinear evolution equations

Kategorie tematyczne

• 65M06: Finite difference methods
• 35K61: Nonlinear initial-boundary value problems for nonlinear parabolic equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1450-1462

Daty

wydano

2017-12-01

otrzymano

2016-04-20

zaakceptowano

2017-06-13

online

2017-12-16

Twórcy

autor

P.G. Dlamini

• , , , ,

autor

M. Khumalo

• , , , ,

Identyfikatory

DOI

10.1515/math-2017-0118