ABSTRACT
This chapter introduces the boundary element method for one–dimensional problems by integrating the fundamental solution of the boundary value problem at the boundary points. Although the boundary element method is more useful in two–dimensional and three–dimensional problems, it clarifies the concepts and the method in the simplest possible geometric setting. The chapter considers one–dimensional potential flow problem (2nd–order equations) and the rectangular beam problem (4th–order equations) to illustrate the method. The theory developed in this chapter is the simplest in the boundary element methods (BEMs) and the results are derived under the assumption that the coefficients a, b, and f are constant. The cases required require the derivation of related fundamental solutions before the BEM becomes applicable.
