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Numerical stability

In numerical modeling, a numerical computational scheme is said to be stable if the infinite set of computed solutions of the discrete algebraic equations created by the process of discretization of some original continuum differential equations is always below some uniformly bounded upper-limit as the computational grid spacing is shrunk to zero. There are reasonably efficacious methods for exploring the stabilility of a given linear set of discretized equations, although it is much trickier with nonlinear equations, with the most popular option for the latter being the linearization thereof.

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