Neutrosophic Sets and Systems
Abstract
This study presents a detailed analysis of the Falkner-Skan equation under uncertainty by employing neutrosophic numbers to represent the uncertainty in no slip conditions and the parameter ��̃. By applying appropriate similarity transformation, partial differential equation (PDE) are converted into ordinary differential equation (ODE). Both the Shooting Method and the Homotopy Perturbation Method (HPM) are utilized to solve ODE’s. These ODE’s are then transmuted into neutrosophic differential equation (NDE) by employing (Α ̃,Β, ̃ Γ ̃)������ approach. The parameter ��̃ and no slip conditions are taken as triangular and trapezoidal neutrosophic numbers. The results are presented graphically to illustrate the comparative effectiveness of these methods. The analysis reveals that use of trapezoidal neutrosophic numbers and triangular neutrosophic numbers in Falkner-Skan equation gives strong neutrosophic solution. A 3D error analysis is conducted to compare the performance of triangular and trapezoidal neutrosophic numbers, highlighting their relative accuracy in solving the Falkner-Skan equation under varying degrees of uncertainty.
Recommended Citation
Amudha, B.; M. Shanmugapriya; R. Sundareswaran; and Said Broumi. "Numerical and Semi Analytical Scheme for developing a solution to Falkner Skan equation in Neutrosophic environments." Neutrosophic Sets and Systems 79, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol79/iss1/11
