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Nonlinear elliptic problems with the method of finite volumes

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  • Sanjay Kumar Khattri

Abstract

We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.

Suggested Citation

  • Sanjay Kumar Khattri, 2006. "Nonlinear elliptic problems with the method of finite volumes," International Journal of Differential Equations, Hindawi, vol. 2006, pages 1-16, October.
    • Handle: RePEc:hin:jnijde:031797
    DOI: 10.1155/DENM/2006/31797
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