1549301742-The_Theory_of_Difference_Schemes__Samarskii

Preliminaries

Conte1nporary methods for solving problems of n1athen1atical physics are

gaining increasing popularity. They are being used more and 1nore in solv-

ing applied problems not only by professional 1nathematicians, but also by

investigators and users working in other branches of science, engineering

and technology. In order to n1ake this book accessible not only to special-

ists, but also to graduate and post-graduate students, we give a complete

account of notions and definitions which will be used in the sequel. The

concepts and theorems presented below are of an auxiliary nature and are

included for references rather than for primary study. For this reason the

majority of statements are quoted without proofs. vVe will also cite biblio-

graphical sources for further, more detailed, information.

1.1 DIFFERENCE EQUATIONS

1. Preliminary comments. By applying approxi1nate methods the problem
   of solving differential equations leads to the systems of linear algebraic
   equations:
   Au=f

where A= (a 1.J. ) is a square (JV x JV)-matrix, u is the vector of unknowns
and f is the right-hand side vector.

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