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Chapter 1: Mathematical Preliminaries

Chapter 1: Mathematical Preliminaries

pp. 3-42

Authors

, Texas A & M University, , Texas A & M University, , Lawrence Livermore National Laboratory, California
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Summary

Most engineering systems can be described, with the aid of the laws of physics and observations, in terms of algebraic, differential, and integral equations. In most problems of practical interest, these equations cannot be solved exactly, mostly because of irregular domains on which the equations are posed, variable coefficients in the equations, complicated boundary conditions, and the presence of nonlinearities. Approximate representation of differential and integral equations to obtain algebraic relations among quantities that characterize the system and implementation of the steps to obtain algebraic equations and their solution using computers constitute a numerical method.

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