Abstract
This chapter reviews the numerical methods for finding solutions to partial differential equations (PDEs). Boundary element method is applicable to most often linear elliptic partial differential equations, often Laplace's equation, and sometimes to parabolic, hyperbolic, or nonlinear elliptic equations. This yields an integral equation. The solution of the integral equation can be 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.
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