Creative telescoping is an algorithmic technique central to computer algebra, employed for deriving recurrence relations and differential equations that characterise definite sums and integrals. By ...

Stochastic differential equations (SDEs) are at the heart of modern financial modelling, providing a framework that accommodates the inherent randomness observed in financial markets. These equations ...

In this paper, we consider the valuation of European and path-dependent options in foreign exchange markets when the currency exchange rate evolves according to the Heston model combined with the ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

The Sinc-Galerkin method originally proposed by Stenger is extended to handle fourth-order ordinary differential equations. The exponential convergence rate of the method, $\mathcal{O}(e^{-\kappa\sqrt ...

In this paper, we present findings concerning the existence of solutions to a particular type of nonlocal second-order delay semilinear integro-differential equation with time-varying evolution. We ...