Stability, consistency, and convergence of numerical discretizations
نویسنده
چکیده
A problem in differential equations can rarely be solved analytically, and so often is discretized, resulting in a discrete problem which can be solved in a finite sequence of algebraic operations, efficiently implementable on a computer. The error in a discretization is the difference between the solution of the original problem and the solution of the discrete problem, which must be defined so that the difference makes sense and can be quantified. Consistency of a discretization refers to a quantitative measure of the extent to which the exact solution satisfies the discrete problem. Stability of a discretization refers to a quantitative measure of the well-posedness of the discrete problem. A fundamental result in numerical analysis is that the error of a discretization may be bounded in terms of its consistency and stability.
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