Topic of Research Seminar: Mathematical Modeling and Exact Solutions for Non-Newtonian Nanofluids and Financial Mathematics

Abstract: The central objective of this dissertation is to provide exact solutions to the complex challenges found in the domains of non-Newtonian nanofluids and financial mathematics. Exact solutions hold a distinct advantage over numerical and experimental counterparts as they offer a clear and precise depiction of the intricate nonlinear formulations. These solutions reveal the significance of various variables within a model and their relative impacts, shedding light on input-output relationships. The Lie symmetry method is a valuable tool employed in this work, enabling the discovery of exact solutions. This method excels in tackling nonlinear differential equations by identifying group transformations that leave a given equation unchanged, effectively determining its underlying symmetries. These symmetries facilitate the mapping of one solution to another, a crucial aspect of this approach. The research presented in this thesis focuses on utilizing the Lie symmetry method to obtain exact solutions for nanofluid flow problems, encompassing a wide array of factors such as fluid flow characteristics, heat transfer processes, and intricate mathematical models originating in financial mathematics. In the context of nanofluid flow, these investigations span various aspects, including diverse flow geometries, boundary conditions, external influences, and surface motions. Simultaneously, in the realm of mathematical finance, where option pricing plays a pivotal role, we encounter the assumption that stock prices follow a standard Brownian motion. This assumption allows us to mathematically model the problem using stochastic differential equations. Under certain idealized conditions, these models transform into parabolic linear partial differential equations with variable coefficients, forming the basis for option valuation. Valuation of options stands as the most prevalent derivative contract in contemporary financial markets.

Subject Field of Topic: Fluid Mechanics and Financial Mathematics

Name of Speaker: Ms. Saba Javaid

Professorial Rank of Speaker: PhD Scholar, Mathematics Dpt. (SNS-NUST)

Email of Speaker: [email protected]

Affiliation of Speaker: School of Natural Sciences (SNS), NUST

Date and Venue: (Friday) 06 October 2023, 1530 hrs, at CR # 202 (New Building SNS), NUST Islamabad Campus