CAUCHY AND FREDHOLM METHODS FOR EULER EQUATIONS,
RAND CORP SANTA MONICA CALIF
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The report demonstrates alternative methods of minimizing a quadratic functional, which is frequently an essential step in the solution of problems in mathematical physics, mechanics, and engineering. Three methods are discussed 1 the classical approach through Euler equations, subject to boundary conditions 2 an approach through the solution of a Fredholm integral equation 3 the initial-value approach, based on the dynamic programming and invariant imbedding. Each method has certain analytic and computational advantages and disadvantages. To illustrate the methods, the study considers the equilibrium configuration of a tightly stretched string, restrained by distributed strings, acted upon by a distributed load, and constrained at the ends in various ways.
- Numerical Mathematics