Solving 3D magnetohydrostatics with RBF-FD: Applications to the solar corona

•A Magnetohydrostatic (MHS) solver is presented using a direct approach to the equation in terms of the magnetic field itself.•It is built on a Radial Basis Function Finite Differences discretization, the first time that method has been applied to MHS.•The solver is tested against an analytic solution that is often used as an initial condition in solar coronal MHD models.•Highly nonlinear magnetic structures are accurately recovered, including discontinuities.•The numerically constructed magnetic field is divergence free to at least 0.0001% of the maximum field strength.