Galerkin Boundary Element Method(GBEM) is a powerful technique to solve partial differential equations. In this work the method is presented by solving the axisymmetric Laplace's equation. Later the Grad-Shafranov Equation(GSE) is solved by means of this powerful technique. The GSE is a simplification of ideal MHD in two dimensions. The resulting equation is a nonlinear, elliptic partial differential equation. The GBEM is well suited for solving this type of equations in 'irregular domains' such as unbounded and irregular shape domains.

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