Solution of the inverse problem for the Grad–Shafranov equation for magnetic field computation in tokamak

The paper suggests a method of solving the inverse problem for the Grad–Shafranov equation with affine right-hand side with non-local condition in cross section of tokamaks and more general domains. A similar problem appears in computation of magnetic field within conventional model of tokamaks. A well-posed statement of the inverse problem is given. Necessary and sufficient conditions of its solvability are set. The used multipole method provided the relative error of the solution and its gradient on the boundary less than $10^{-9}$ by the use of about $100$ degrees of freedom.