Extension of the method of generalized quasilinearization for second order boundary value problems

Abstract

In this paper the method of generalized quasilinearization has been extended to second order nonlinear boundary value problem. We develop the method of quasilinearization when the right hand side function is the sum of a convex and a concave function. Yet like monotone method, we have two sided moriotone iteraterates which converges quadratically to the unique solution of the boundary value problem.

Keywords:

• Upper and lower solutions
• convex and convex functions

¹Permanent address: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

¹Permanent address: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Notes

¹Permanent address: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan