Second order differential equations with Dirichlet boundary conditions

Abstract

In this paper we use a quasilinearization method to find an approximate solution of a nonlinear Dirichlet problem for second order differential equations. Sufficient conditions are formulated to obtain weak-quadratic, semi-quadratic or quadratic convergence of approximate solutions.

Keywords:

• Dirichlet boundary conditions
• Second order differential equations
• Approximate solutions
• Quasilinearization
• Convergence