ABSTRACT
Application problems in engineering practice may not be easily solved by certain techniques, if solvable at all. Before this chapter embarks on applications, it discusses solution techniques that are amenable for practical problems. These methods produce approximate solutions and are, as such, called numerical methods. It was mentioned in the introduction that the solution of the Euler-Lagrange differential equation resulting from a certain variational problem may not be easy. This gave rise to the idea of directly solving the variational problem. The classical method is the Euler method. The chapter discusses the Ritz method, which is based on an approximation of the unknown solution function with a linear combination of certain basis functions. It demonstrates that the solution function satisfies the zero boundary condition on the circumference of the square. The boundary integral method, which is related to the Kantorovich's method, is also discussed.
