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Abstract
The paper concerns with the computational algorithms for a steady-state reaction diffusion problem. A lagged diffusivity iterative algorithm is proposed for solving resulting system of quasilinear equations from a finite difference discretization. The convergence of the algorithm is discussed and the numerical results show the efficiency of this algorithm.
Highlights
We consider the problem of finding a solution of the system of nonlinear equations
We consider the solution of the system of quasilinear equations
In problems related with the study of reaction and diffusion processes that can be described by nonlinear partial differential equations of elliptic type (e.g., [1], [11], [14])
Summary
We consider the problem of finding a solution of the system of nonlinear equations. F (u) = 0, where F : Ω ⊆ Rn → Rn is a continuously differentiable mapping. We are interested in large scale systems for which the Jacobian of F is not available or is difficult to compute. We consider the solution of the system of quasilinear equations. Where A(u) is a real matrix of order n and G : Ω ⊆ Rn → Rn is a continuously differentiable mapping. The systems of the form (1) appear in many problems of practical interest. In problems related with the study of reaction and diffusion processes that can be described by nonlinear partial differential equations of elliptic type (e.g., [1], [11], [14])
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