Existence and uniqueness of solutions of certain systems of algebraic equations with off diagonal nonlinearity
- Fuhrmann, Jürgen
2010 Mathematics Subject Classification
- 65M12 65H10 15A48 65E99
- systems of algebraic equations, positive matrices, viscous conservation laws, finite volume methods, nonlinear parabolic PDEs
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.
- Applied Numerical Mathematics, 37 (3):357-368, 2001