The numerical solution of elliptic equations

Garret Birkhoff9780686242512, 9780898710014, 0686242513, 0898710014

A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing — the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.

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Table of contents :
The NUMERICAL SOLUTION Of ELLIPTIC EQUATIONS……Page 1
Contents……Page 5
Acknowledgments……Page 7
Preface……Page 9
General References……Page 11
LECTURE 1 Typical Elliptic Problems……Page 13
LECTURE 2 Classical Analysis……Page 23
LECTURE 3 Difference Approximations……Page 31
LECTURE 4 Relaxation Methods……Page 41
LECTURE 5 Semi-iterative Methods……Page 51
LECTURE 6 Integral Equation Methods……Page 59
LECTURE 7 Approximation of Smooth Functions……Page 67
LECTURE 8 Variational Methods……Page 75
LECTURE 9 Applications to Boundary Value Problems……Page 85