Solving singular nonlinear boundary value problems by combining the homotopy perturbation method and reproducing kernel Hilbert space method

Abstract

This paper investigates singular nonlinear boundary value problems (BVPs). The numerical solutions are developed by combining He's homotopy perturbation method (HPM) and reproducing kernel Hilbert space method (RKHSM). He's HPM is based on the use of traditional perturbation method and homotopy technique. The HPM can reduce a nonlinear problem to a sequence of linear problems and generate a rapid convergent series solution in most cases. RKHSM is also an analytical technique, which can solve powerfully singular linear BVPs. Therefore, we solve singular nonlinear BVPs using advantages of these two methods. Three numerical examples are presented to illustrate the strength of the method.

Keywords:

• singular
• nonlinear boundary value problems
• homotopy perturbation method
• reproducing kernel Hilbert space method

AMS Subject Classification :

• 34K10
• 34M35
• 47B32
• 34K28
• 47J25

Acknowledgements

This work was supported by National Natural Science Foundation of China (60572125).