WIAS Preprint No. 425, (1998)

Existence and uniqueness of solutions of certain systems of algebraic equations with off diagonal nonlinearity



Authors

  • Fuhrmann, Jürgen
    ORCID: 0000-0003-4432-2434

2010 Mathematics Subject Classification

  • 65M12 65H10 15A48 65E99

Keywords

  • systems of algebraic equations, positive matrices, viscous conservation laws, finite volume methods, nonlinear parabolic PDEs

Abstract

Using inverse positivity properties and Brouwer's fixed point theorem, we derive existence and uniqueness results for certain nonlinear systems of equations with off diagonal nonlinearity. The type of systems considered arises from stable finite volume discretizations of viscous nonlinear conservation laws and has a wide range of applications.

Appeared in

  • Applied Numerical Mathematics, 37 (3):357-368, 2001

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