Spline solution of non-linear singular boundary value problems

Abstract

A class of non-linear singular boundary value problems is solved by new methods based on non-polynomial cubic spline. We use the quasilinearization technique to reduce the given non-linear problem to a sequence of linear problems. We modify the resulting set of differential equations at the singular point then treat this set of boundary value problems by using a non-polynomial cubic spline approximation. Convergence of the methods is shown through standard convergence analysis. Numerical examples are given to illustrate the applicability and efficiency of our methods.

Keywords:

• Non-linear ordinary differential equation
• Non-polynomial cubic spline
• Convergence analysis
• Physiology applications

Additional information

Notes on contributors

R. Mohammadi

Email: [email protected]

R. Jalilian

Email: Email: [email protected]