Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 90, pp. 1-12.

Title: Generalized quasilinearization method for a second 
       order three point boundary-value problem with 
       nonlinear boundary conditions
        
Authors: Bashir Ahmad (King Abdulaziz Univ. Saudi Arabia)
         Rahmat Ali Khan (Quaid-i-Azam Univ., Pakistan)
         Paul W. Eloe (Univ. of Dayton, OH, USA)
         
Abstract: 
  The generalized quasilinearization technique is applied to
  obtain a monotone sequence of iterates converging uniformly and
  quadratically to a solution of three point boundary value problem
  for second order differential equations with nonlinear boundary
  conditions. Also, we improve the convergence of the sequence of
  iterates by establishing a convergence of order $k$.
     
Submitted March 14, 2002. Published October 22, 2002.
Math Subject Classifications: 34B10, 34B15.
Key Words: Generalized quasilinearization; boundary value problem;
    nonlinear boundary conditions; quadratic and rapid convergence.