Rotated Outer-Inner Iterative Schemes for The Solution of Burgers' Equation

Abstract

Dalam kertas kerja mereka, Ali dan Abdullah telah memperkenalkan kaedah-kaedah lelaran baru berdasarkan pendiskretan beza terhingga lima titik putaran dalam menyelesaikan sistem berpasangan persamaan pembezaan separa \textit{eliptik} di mana kaedah-kaedah ini telah didapati lebih baik daripada kaedah sedia ada yang berdasarkan skema beza terhingga ke tengah. Dalam kertas ini, aplikasi skema lelaran baru yang diterbitkan daripada pendiskretan beza terhingga putaran ini kepada penyelesaian berangka persamaan Burgers dua dimensi tak linear telah ditinjau. Beberapa ujikaji berangka akan dibentangkan dan kami akan menunjukkan bahawa kaedah-kaedah baru ini adalah jitu dan setanding dengan kaedah beza terhingga yang sedia ada. Katakunci: Kaedah berangka; persamaan Burgers; beza terhingga putaran; kaedah kumpulan nyah pasangan tak tersirat (KNPTT) In their paper, Ali and Abdullah introduced new iterative methods based on \textit{rotated(cross)} five-point finite difference discretisation in solving a coupled system of \textit{elliptic} partial differential equations (p.d.e.'s) where these methods were found to be more superior than common existing methods based on the \textit{centred} five-point difference schemes. In this paper, the application of a new iterative schemes derived from the \textit{rotated} finite difference discretisation to the numerical solution of the nonlinear steady two dimensional Burgers' equation is considered. Some numerical experiments are presented and we will show that the new methods are accurate and comparable to the existing finite difference method. Keywords: Numerical methods; Burgers' equation; rotated finite difference; explicit decoupled group (EDG) method