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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 GradShafranov 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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