Computational solution of nonlinear operator equations - ISBN:0471706604

Computational solution of nonlinear operator equations

Date: 12 April 2011, 04:39

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The applied mathematician and the numerical analyst of today are faced with the problem of finding solutions, or at least approximate solutions of sufficient accuracy, of what may seem to be a bewildering variety of equations: finite and infinite systems, ordinary and partial differential equations subject to initial or boundary conditions, or their combination, and integral or integrodifferential equations. To complicate the matter further many of these equations are nonlinear. From the standpoint of functional analysis, however, all may be formulated in terms of operators that map some linear space into itself, the solutions being sought as elements or points in the corresponding space. Consequently computational methods that work in this general setting for the solution of equations apply to a large number of problems and lead directly to the development of effective and reliable computer programs to obtain accurate approximate solutions to equations in the original or a related space.

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