Abstract
This chapter focuses on boundary element method applicable to mostly linear elliptic partial differential equations, often to Laplace's equation and sometimes to parabolic, hyperbolic, or nonlinear elliptic equations. An integral equation is obtained. The solution of the integral equation is used in an integral representation of the solution. The problem of solving a partial differential equation within a given domain can be transformed into one solving an equivalent integral equation on the boundary of the domain. The unknown in the integral equation will be the charge density on the boundary of the domain. After the boundary integral equation has been formulated, it is often solved numerically.
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