MA 7006 Numerical Methods: Convergence and Stability Theory
The basic concepts of the asymptotic theory of discretization methods are defined in such a way that convergence is always equivalent to consistency and stability. The theory is then applied to a discretization method, a kind of initial value problem for an ordinary differential equation, the so-called weak nonlinear method.
The MA 7006 Numerical Methods: Convergence and Stability Theory course provides students with the overview of the application of theories from dynamical systems to the analysis of numerical methods for initial-value problems. The course mainly emphasizes the explanation of the classical viewpoints of numerical analysis and of dynamical systems and then exhibit how the two viewpoints can be combined to offer a framework for both the interpretation of data obtained from numerical simulations and the design of efficient numerical methods.
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