This chapter addresses problems that may not be easily solved by analytic techniques, if solvable at all. Hence, before we embark on applications in later chapters, we discuss techniques that provide approximate solutions for such problems.
The discussion starts with the classical method of this class, the Euler method, and the most influential method, that of Ritz’s. The methods of Galerkin and Kantorovich follow, both described in [10]. They could be considered extensions of Ritz’s. Finally, the boundary integral and the finite element methods, the most well-known by engineers and used in the industry, conclude the chapter.
Euler proposed a numerical solution for the variational problem of
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