Development of numerical tools using boundary element method based on Taylor series for nonlinear analysis

• DOI: 10.1142/s0217984923500501
• Publication Date: 2023-04-28T01:29:56Z
• Authors: M. Ramzan; M. O. Ahmad; M. N. Bashir; A. Asghar; S. A. Shehzad
• Keywords: 0103 physical sciences; 01 natural sciences

The major theme of this research is to develop the numerical scheme for the computation of nonlinear problems by the implementation of the boundary element method dependent on Taylor’s series. This paper deals with the problem of laminar flow in a semiporous channel in the presence of a transverse magnetic field and the homotopy analysis method (HAM) is employed along with the general boundary element method to compute an approximated solution of the system of nonlinear differential equation governing the problem concerned. A well-known and useful nonlinear differential equation of fluid mechanics [Formula: see text] with the boundary conditions [Formula: see text], [Formula: see text] is referred as an example to show a glimpse into the basic idea of the method and technique used in this paper. It shows the capabilities and wide range of applications of HAM using Taylor series expansion of the derived integral equation. A comparison of HAM with the results calculated previously has been discussed. The solution obtained with HAM in comparison with the numeric solution shows remarkable accuracy. Root mean square formula is computed for the convergence analysis at various values. An increment in the number of elements depicting the convergent results as error is decreased.