JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SOLVING SINGULAR NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS IN THE REPRODUCING KERNEL SPACE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
SOLVING SINGULAR NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS IN THE REPRODUCING KERNEL SPACE
Geng, Fazhan; Cui, Minggen;
  PDF(new window)
 Abstract
In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation to the exact solution u(x) is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.
 Keywords
exact solution;singular nonlinear boundary value problem;reproducing kernel;
 Language
English
 Cited by
1.
REPRODUCING KERNEL METHOD FOR SOLVING TENTH-ORDER BOUNDARY VALUE PROBLEMS,;;

Journal of applied mathematics & informatics, 2010. vol.28. 3_4, pp.813-821
1.
An Approximation Method for Solving Volterra Integrodifferential Equations with a Weighted Integral Condition, Journal of Function Spaces, 2015, 2015, 1  crossref(new windwow)
2.
Solving a system of linear Volterra integral equations using the new reproducing kernel method, Applied Mathematics and Computation, 2013, 219, 20, 10225  crossref(new windwow)
3.
RKM for solving Bratu-type differential equations of fractional order, Mathematical Methods in the Applied Sciences, 2016, 39, 6, 1548  crossref(new windwow)
4.
A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems, Applied Mathematics and Computation, 2009, 213, 1, 163  crossref(new windwow)
5.
A novel method for nonlinear two-point boundary value problems: Combination of ADM and RKM, Applied Mathematics and Computation, 2011, 217, 9, 4676  crossref(new windwow)
6.
Construction and calculation of reproducing kernel determined by various linear differential operators, Applied Mathematics and Computation, 2009, 215, 2, 759  crossref(new windwow)
7.
Approximate Solutions to Three-Point Boundary Value Problems with Two-Space Integral Condition for Parabolic Equations, Abstract and Applied Analysis, 2012, 2012, 1  crossref(new windwow)
8.
New Implementation of Reproducing Kernel Method for Solving Functional-Differential Equations, Applied Mathematics, 2016, 07, 10, 1074  crossref(new windwow)
9.
Solving a System of Linear Volterra Integral Equations Using the Modified Reproducing Kernel Method, Abstract and Applied Analysis, 2013, 2013, 1  crossref(new windwow)
10.
Solving Fredholm integro–differential equations using reproducing kernel Hilbert space method, Applied Mathematics and Computation, 2013, 219, 17, 8938  crossref(new windwow)
11.
A numerical solution to nonlinear multi-point boundary value problems in the reproducing kernel space, Mathematical Methods in the Applied Sciences, 2011, 34, 1, 44  crossref(new windwow)
12.
Application of reproducing kernel method to third order three-point boundary value problems, Applied Mathematics and Computation, 2010, 217, 7, 3425  crossref(new windwow)
13.
Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method, Applied Mathematics and Computation, 2009, 215, 6, 2095  crossref(new windwow)
14.
The exact solution of a class of Volterra integral equation with weakly singular kernel, Applied Mathematics and Computation, 2011, 217, 18, 7515  crossref(new windwow)
15.
A novel method for nonlinear singular fourth order four-point boundary value problems, Computers & Mathematics with Applications, 2011, 62, 1, 27  crossref(new windwow)
16.
A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems, Journal of Computational and Applied Mathematics, 2015, 279, 293  crossref(new windwow)
17.
Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations, Abstract and Applied Analysis, 2012, 2012, 1  crossref(new windwow)
18.
Picard-Reproducing Kernel Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-Emden Type Equations, Mathematical Modelling and Analysis, 2015, 20, 6, 754  crossref(new windwow)
19.
Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods, Nonlinear Analysis: Real World Applications, 2010, 11, 2, 637  crossref(new windwow)
20.
Homotopy perturbation–reproducing kernel method for nonlinear systems of second order boundary value problems, Journal of Computational and Applied Mathematics, 2011, 235, 8, 2405  crossref(new windwow)
 References
1.
R. P. Agarwal and D. O'Regan, Second-order boundary value problems of singular type, J. Math. Anal. Appl. 226 (1998), no. 2, 414-430 crossref(new window)

2.
M. K. Kadalbajoo and V. K. Aggarwal, Numerical solution of singular boundary value problems via Chebyshev polynomial and B-spline, Appl. Math. Comput. 160 (2005), no. 3, 851-863 crossref(new window)

3.
P. Kelevedjiev, Existence of positive solutions to a singular second order boundary value problem, Nonlinear Anal. 50 (2002), no. 8, Ser. A: Theory Methods, 1107-1118 crossref(new window)

4.
C. Li and M. Cui, The exact solution for solving a class nonlinear operator equations in the reproducing kernel space, Appl. Math. Comput. 143 (2003), no. 2-3, 393-399 crossref(new window)

5.
Y. Liu and A. Qi, Positive solutions of nonlinear singular boundary value problem in abstract space, Comput. Math. Appl. 47 (2004), no. 4-5, 683-688 crossref(new window)

6.
Y. Liu and H. Yu, Existence and uniqueness of positive solution for singular boundary value problem, Comput. Math. Appl. 50 (2005), no. 1-2, 133-143 crossref(new window)

7.
R. K. Mohanty, P. L. Sachdev, and N. Jha, An O($h^4$) accurate cubic spline TAGE method for nonlinear singular two point boundary value problems, Appl. Math. Comput. 158 (2004), no. 3, 853-868 crossref(new window)

8.
A. S. V. Ravi Kanth and Y. N. Reddy, Higher order finite difference method for a class of singular boundary value problems, Appl. Math. Comput. 155 (2004), no. 1, 249-258 crossref(new window)

9.
A. S. V. Ravi Kanth and Y. N. Reddy, Cubic spline for a class of singular two-point boundary value problems, Appl. Math. Comput. 170 (2005), no. 2, 733-740 crossref(new window)

10.
J. Wang, W. Gao, Z. Zhang, Singular nonlinear boundary value problems arising in boundary layer theory, J. Math. Anal. Appl. 233 (1999), no. 1, 246-256 crossref(new window)

11.
X. Xu and J. Ma, A note on singular nonlinear boundary value problems, J. Math. Anal. Appl. 293 (2004), no. 1, 108-124 crossref(new window)

12.
X. Zhang and L. Liu, Positive solutions of superlinear semipositone singular Dirichlet boundary value problems, J. Math. Anal. Appl. 316 (2006), no. 2, 525-537 crossref(new window)