On the performance of certain direct and iterative methods on equations arising on a two-dimensional in situ combustion simulator

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Bahadir A. R., ELLERBY F.

APPLIED MATHEMATICS AND COMPUTATION, vol.125, pp.347-358, 2002 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 125
• Publication Date: 2002
• Doi Number: 10.1016/s0096-3003(00)00136-3
• Journal Name: APPLIED MATHEMATICS AND COMPUTATION
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.347-358
• Inonu University Affiliated: Yes

Abstract

A two-dimensional mathematical model of the in situ combustion process involves a set of nonlinear partial differential equations. These equations are discretized in implicit finite-difference form. The resulting set of nonlinear algebraic equations are solved for each time-step by use of a Newton-Raphson procedure. Each Newton iteration produces an equation of the form