In this article, the applications of the improved residual power series method (IRPSM) and its enhanced version incorporating Adomian polynomials (AP) to solve boundary value problems (BVPs) of higher orders are presented.
To show the efficacy and computational efficiency of both approaches, five case studies including those from the fourth, fifth, sixth, tenth and thirteenth orders, are provided.
The findings obtained indicate that the IRPSM with AP is a more efficient option than the normal IRPSM since it greatly decreases CPU time while retaining greater accuracy. The introduction of Adomian polynomials in a novel approach applied for the first time in this case study proves to be a valuable innovation for solving complex nonlinear BVPs. This work highlights the potential of IRPSM with AP in numerical analysis, offering a faster and more reliable solution method for a wide range of problems.
To the best of our knowledge, IRPSM is applicable only to finite boundary value problems (BVPs). The same limitation applies to IRPSM with Adomian polynomials, as Adomian polynomials primarily serve to enhance convergence and reduce computational costs rather than extending the method’s applicability to infinite or unbounded domains.
The novelty of this article lies in its innovative approach to solving higher-order BVPs efficiently. By incorporating the Adomian polynomials (AP), this method enhances the IRPSM, significantly reducing the computational time while maintaining higher accuracy. This new integration is a significant addition to the area of numerical analysis as it offers a more dependable and efficient way to solve complicated nonlinear BVPs. For the first time, Adomian polynomials are used in this way, presenting a potentially useful tool for solving higher-order and nonlinear problems that are difficult for conventional approaches to solve effectively. Research objectives: The objectives of this research are to: Investigate the effectiveness of IRPSM when combined with AP for solving higher-order BVPs? Compare and evaluate the computational efficiency and accuracy of IRPSM with AP against traditional IRPSM. Apply IRPSM with AP to test problems of 4th, 5th, 6th, 10th and 13th orders and demonstrate its ability to reduce CPU time while preserving accuracy.
The IRPSM with Adomian polynomials enhances the accuracy of solutions for higher-order BVPs.
IRPSM with Adomian polynomials is a more efficient approach compared to IRPSM.
The IRPSM with Adomian polynomials improves convergence speed and stability, ensuring faster and more reliable solutions.
