Iterative Method for Solving 2D Laplace'S Equation With a Polynomial Boundary Condition

ABSTRACT M. Jaoua et al. investigated the linear approximation of the Robin problem on , an open bounded domain in , and established several significant results. In this paper, we extend their work by studying a nonlinear approximation of an elliptic problem with a nonlinear Robin boundary condition in a two‐dimensional domain . Using an iterative construction method and imposing an admissible condition on the boundary , we prove the existence and uniqueness of the solution.