Reproducing kernel method in Hilbert spaces for solving the linear and nonlinear four-point boundary value problems

ABSTRACT

An analysis was performed in this paper to study the problem of magnetohydrodynamic squeezing flow of nanofluid between parallel disks. This paper also proposed a reproducing kernel method for solving fourth-order four-point boundary value problems. In order to eliminate the singularity of the equation, a transform was used. Convergence analysis and error estimation for the present method in $L^2$-space were also discussed. The exact solution was represented in the form of series in the reproducing kernel Hilbert space which proved higher accuracy in numerical computation. The algorithm derived from this approach can be easily implemented. The ideas and techniques presented in this paper will be useful for solving many other problems.

KEYWORDS:

• Squeezing flow
• reproducing kernel method
• approximate solution
• convergence analysis
• four-point boundary value problem

2010 AMS SUBJECT CLASSIFICATIONS:

• 35A24
• 46E20
• 47B32

Acknowledgements

The authors would like to thank the editor-in-chief of the journal Professor Qin Sheng and the reviewers for their precious time and invaluable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.