ABSTRACT: We use the Power Series Method (PSM) numerical framework for estimating nonlinear variations of the Black-Scholes partial differential equations (PDE). The PSM offers an alternative to using ...

Corresponding to the link of Itô's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker–Planck equations. This ...

EVEN from the point of view of an undergraduate, the subject of differential equations is very diiferent from what it was fifty years ago. But in a large and miscellaneous collection of examples like ...

Abstract: Finite difference methods are well‐known numerical methods to solve differential equations by approximating the derivatives using different difference schemes. Theoretical results have been ...

This project was undertaken as a dissertation for a Master's programme in Mathematics at Durham University (Oct. 2022 - Apr. 2023), where it attained a final grade of 85%. The report will be ...