JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Approximating Coupled Solutions of Coupled PBVPs of Non-linear First Order Ordinary Differential Equations
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 1,  2016, pp.221-233
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.1.221
 Title & Authors
Approximating Coupled Solutions of Coupled PBVPs of Non-linear First Order Ordinary Differential Equations
Dhage, Bapurao Chandrabhan;
  PDF(new window)
 Abstract
The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.
 Keywords
Coupled Periodic boundary value problems;Coupled fixed point theorem;Dhage iteration principle;Approximate coupled solutions;
 Language
English
 Cited by
 References
1.
B. C. Dhage, Periodic boundary value problems of first order Caratheodory and discontinuous differential equations, Nonlinear Funct. Anal. & Appl., 13(2)(2008), 323-352.

2.
B. C. Dhage, Hybrid fixed point theory in partially ordered normed linear spaces and applications to fractional integral equations, Differ. Equ. Appl., 5(2013), 155-184.

3.
B. C. Dhage, Partially condensing mappings in partially ordered normed linear spaces and applications to functional integral equations, Tamkang J. Math., 45(4)(2014), 397-426. crossref(new window)

4.
B. C. Dhage, Nonlinear D-set-contraction mappings in partially ordered normed linear spaces and applications to functional hybrid integral equations, Malaya J. Mat., 3(1)(2015), 62-85.

5.
B. C. Dhage, Operator theoretic techniques in the theory of nonlinear hybrid differential equations, Nonlinear Anal. Forum, 20(2015), 15-31.

6.
B. C. Dhage, S. B. Dhage, Approximating solutions of nonlinear first order ordinary differential equations, GJMS Special issue for Recent Advances in Mathematical Sciences and Applications-13, GJMS 2(2)(2014), 25-35.

7.
B. C. Dhage, S. B. Dhage, Coupled hybrid fixed point theorems in partially ordered metric spaces with application, Nonlinear Studies, 21(4)(2014), 675-686.

8.
B. C. Dhage, S. B. Dhage, Approximating solutions of nonlinear pbvps of hybrid differential equations via hybrid fixed point theory, Indian J. Math., 57(1)(2015), 103-119.

9.
B. C. Dhage, S. B. Dhage, Approximating positive solutions of pbvps of nonlinear first order ordinary quadratic differential equations, Appl. Math. Lett. 46(2015), 133-142. crossref(new window)

10.
B. C. Dhage, S. B. Dhage, A new iteration principle in the theory of PBVPs of nonlinear first order integro-differential equations, Adv. Nonlinear Var. Inequ., 18(2)(2015), 20-39.

11.
T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: TMA 65(2006), 1379-1393.

12.
D. Guo, V. Lakshmikantham, Coupled fixed point of nonlinear operators with applicatons, Nonlinear Anal., 11(1987), 623-632. crossref(new window)

13.
S. Heikkila, V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker inc., New York 1994.

14.
Y. Sun, A fixed point theorem for mixed monotone operator with applications, J. Math. Anal. Appl., 156(1991), 240-252. crossref(new window)