Numerical solution for the nonlinear eigenvalue problems in bifurcation points

In this article we propose a numerical Picard’s method to solve the nonlinear eigenvalue problem in its bifurcation point. The Picard’s method is used to linearize the problem. The problem is solved using five-point finite difference method. Two general example problems are solved and numerical results are given. Numerical results are compared with theoretical aspects of the bifurcation point of specific kind of nonlinear eigenvalue problems.