An in-depth analysis of the IRPSM-Padé algorithm for solving three-dimensional fluid flow problems

Abstract

In this article, a comparative analysis of the IRPSM-Padé and DTM-Padé methods has been conducted by solving the fluid flow problem over a bi-directional extending sheet. The fluid flow is expressed by the partial differential equations (PDEs) which are then converted to ordinary differential equations (ODEs) by mean of similarity variables. Both the IRPSM-Padé and DTM-Padé methods are tested at [3,3] and [6,6] Padé approximants. Tables and Figures are used to examine the outcomes and show the consistency and accuracy of both approaches. The outcomes of IRPSM-Padé [3,3] and [6,6] with the same order of approximations closely match the outcomes of DTM-Padé [3,3] and [6,6] using Padé approximants. The significant degree of agreement between the two methods indicates that IRPSM-Padé and DTM-Padé handle the fluid flow problem in a comparable manner. The findings of the IRPSM-Padé and DTM-Padé methods show a strong degree of agreement, indicating the accuracy and dependability of the more recent technique (IRPSM-Padé). The obtained CPU time shows that the DTM consistently perform better that IRPSM in terms of computational efficiency. The total CPU time for IRPSM is nearly three-times greater than that of DTM, indicating that IRPSM demands more computational effort. The recorded times accurately reflect the computational efficiency of IRPSM and DTM because the Padé approximation simply improves the results rationalization and has no influence on CPU time. The residual errors analysis demonstrates that the IRPSM-Padé technique produces exceptionally precise approximations, with errors decreasing as the Padé order increases. Furthermore, the numerical assessment demonstrates that higher Padé orders improve the accuracy and stability of the IRPSM-Padé.

Computational Implementation:

Mathematica 14.1 was used to carry out numerical simulations, the DTM-Padé method, and the IRPSM-Padé method. Mathematica’s integrated symbolic and numerical solvers, including the ND Solve function for numerical validation, were used to solve the governing equations. Additionally, plots, such as mesh visualizations and absolute error graphs, were created using Mathematica’s built-in plotting capabilities without the usage of third-party programs.