Solving of nonlinear equations which arise in collocation method
The paper concerns a Dirichlet problem for the equation - A.u + F(x,y,u,ux,Uy) = 0'on a rectangle. An iteration process for solving a nonlinear system of algebraic equations which arise in collocation method is considered. A convergence and an error estimate are obtained. Numerical results are presented for equations with F=cu+eu+f(x,y).