Least Square Homotopy Perturbation Method for Ordinary Differential Equations

In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. To analyze the efficiency of the proposed scheme, tested problems have also been solved through HPM and results are compared with LSHPM. Furthermore, obtained results are also compared with other numerical schemes available in literature. Analysis reveals that LSHPM is a consistent and effective scheme which can be used for more complex BVPs in science and engineering.

Automated summary

A new modification of the homotopy perturbation method, called the least square homotopy perturbation method (LSHPM), is introduced in this study for solving various order boundary value problems. The LSHPM is tested against linear and nonlinear differential equations of second to seventh order, showing its effectiveness and consistency for complex BVPs in science and engineering. The results obtained from LSHPM are compared with those from other numerical schemes as well as the traditional HPM, confirming the efficiency of the proposed scheme.