A reliable algorithm for higher order boundary value problems

In this manuscript, extension of residual power series method (RPSM) is proposed for ordinary differential equations with boundary conditions. The extended algorithm is tested against different boundary value problems (BVPs), and results are compared with other schemes to show the reliability of proposed methodology. Analysis reveals that extended approach can easily handle BVPs and provide convergent series solution without discretization, perturbation or linearization. Hence, practically RPSM is better choice for scientists and researchers working in different field of engineering and sciences.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

In this paper, an extended residual power series method (RPSM) is proposed to solve ordinary differential equations with boundary conditions. The reliability of the proposed methodology is tested by comparing the results with other schemes for different boundary value problems (BVPs). The analysis shows that the extended approach can handle BVPs easily and provide a convergent series solution without the need for discretization, perturbation, or linearization. Therefore, RPSM is a better choice for scientists and researchers working in various fields of engineering and sciences.