A Method for Numerical Solution of Two Point Boundary Value Problems with Mixed Boundary Conditions

Pramod Kumar Pandey^1,2

¹Department of Mathematics, Dyal Singh College (Univ. of Delhi), New Delhi , India.
²Present Address: Department of Information Technology, College of Applied Sciences, Ministry of Higher Education, Salalah, Sultanate of Oman.

DOI: 10.4236/oalib.1100565                

Abstract

In this article, we concerned with the development of a method for solving two point boundary value problems of ordinary differential equations. To develop method, we consider derivative of solution of a problem as an intermediate problem (IP). The analytical solution of the problem and IP were locally approximated by a nonlinear function with fixed step length. Some numerical experiments have been carried out to show the performance and effectiveness of the proposed method. Also we obtained numerical value of derivative of solution as a byproduct of proposed method. A clear conclusion can be drawn from the results that method converges with limited stability.

Keywords

Approximations, Boundary Value Problems, Fixed Step Size, Mixed Boundary Conditions, Maximum Absolute Error, Nonlinear Function, Stability

Conflicts of Interest

The authors declare no conflicts of interest.

References

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