The generalized quasilinearization technique for a second order differential equation with separated boundary conditions

• Published in: Mathematical and computer modelling Vol. 43; no. 7; pp. 727 - 742
• Main Author: Khan, Rahmat Ali
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-04-2006; Elsevier Science
• Subjects: Exact sciences and technology; General boundary conditions; Mathematical analysis; Mathematics; Ordinary differential equations; Quasilinearization; Rapid convergence; Sciences and techniques of general use; Upper and lower solutions; Rapid convergence; Upper and lower solutions; Quasilinearization; General boundary conditions; Second order equation; Monotonic solution; Differential equation; Nonlinear differential equations; Boundary condition; Convergence; Non linear equation; Applied mathematics; Quasilinearization method
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2005.05.017

The method of upper and lower solutions and the method of quasilinearization for a second order nonlinear differential equation
−
x
″
(
t
)
=
f
(
t
,
x
,
x
′
)
,
t
∈
[
0
,
1
]
subject to the separated boundary conditions
p
0
x
(
0
)
−
q
0
x
′
(
0
)
=
a
,
p
1
x
(
1
)
+
q
1
x
′
(
1
)
=
b
, is developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained.