![]() ![]() ![]() We show that each problem can be alleviated by using the two schemes together in a hybrid scheme. Both Picard and Newton iterations commonly used to solve the nonlinear GS equation can exhibit convergence problems. The accuracy of our methods is demonstrated by comparing our numerical solutions with several analytic solutions of linear GS equations. Eliminating the outer iterations of the traditional algorithms based on, for example, Von Hagenow’s method can make the calculation for the free-boundary problem much more straightforward and easier. Using this new mapping technique, the nonlinear Grad–Shafranov (GS) equation can be solved using only the “inner iterations” but with the actual boundary condition at infinity. A novel mapping of the semi-bounded ( R, Z ) domain to a finite computational domain is used to solve the free-boundary axisymmetric equilibrium problem for tokamaks.
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