The Carleman Contraction Mapping Method for Quasilinear Elliptic Equations with Over-determined Boundary Data

We propose a globally convergent numerical method to compute solutions general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility suitable Carleman weight function, we define map which fixed point is solution PDE under consideration. To find this point, recursive sequence an arbitrary initial term using same manner as in proof contraction principle. Applying estimate, show that above converges desired solution. On other hand, also our delivers reliable even when given data are noisy. Numerical examples presented.