ON THE STABILITY ANALYSIS AND NUMERICAL DYNAMICS OF THE NONLINEAR BLACK-SCHOLES EQUATION IN CONFORMABLE ARISING IN ECONOMY - Chen, Qiliang; Yokus, Asif; Baskonus, Haci mehmet; Gao, Wei (World Scientific Publ Co Pte Ltd, 2026)
This paper extracts entirely new complex logarithmic prototypes to the nonlinear Black-Scholes equation used to investigate the price in economy. Newly submitted to the literature, (1/G ')-expansion method is used, successfully. Complex, logarithmic and hyperbolic non-traveling wave solutions are extracted to the considered model. Examined is the solution's response for various conformable operator values. To verify the sensitivity of the numerical outcomes, tables with the stability and absolute error analysis findings are also provided. Von Neumann Stability analysis looks at the circumstances in which the model's numerical findings are stable. Critical features, such as stability analysis and error evaluation, are presented, providing comprehensive information on the reliability and accuracy of the method. Errors that arise during the approximation process and the impact of parameter values are displayed through tables and graphs when employing the numerical technique. It offers a thorough comprehension of the financial phenomenon that the model under examination represents.
Keywords: Nonlinear Black-Scholes Equation; Conformable Operator; (1/G ')-Expansion Method; Complex Logarithmical and Hyperbolic Non-Traveling Wave Solutions; Contour Graphs; Stability Analysis