Newton type methods for solving a Hasegawa–Mima plasma model

In Karakazian and Nassif (2019), the non-linear space-time Hasegawa–Mima plasma equation is formulated as a coupled system of two linear PDEs, solution which pair (u,w), with w=(I−Δ)u. The first hyperbolic type second elliptic type. Variational frames for obtaining weak solutions to initial value problem periodic boundary conditions were also derived. more recent work et al. (2022), numerical approach consisting finite element space-domain combined an Euler-implicit time scheme was used discretize variational model. A semi-linear version this implicit nonlinear tested several types conditions. This proved lack efficiency long time, necessitates imposing cap on magnitude solution. To circumvent difficulty, in paper, we use Newton-type methods (Newton, Chord introduced Modified Newton method) solve numerically fully-implicit scheme. Testing these FreeFEM++ indicates significant improvements no needs be imposed time. sequel, demonstrate validity by proving results, particular convergence implemented methods.