This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

Elliptic partial differential equations (PDEs) are a central pillar in the mathematical description of steady-state phenomena across physics, engineering, and applied sciences. Characterised by the ...

Discontinuous Galerkin (DG) methods represent a versatile and robust class of numerical schemes for approximating solutions to partial differential equations (PDEs). Combining elements of finite ...

SIAM Journal on Numerical Analysis, Vol. 7, No. 1 (Mar., 1970), pp. 47-66 (20 pages) Linear one step methods of a novel design are given for the numerical solution of stiff systems of ordinary ...

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

Cheng, R. , Liu, J. , Hao, L. and Wu, D. (2026) On the Application of the Infinitesimal Method to Two Categories of Problems in College Physics. Open Journal of Social Sciences, 14, 378-389. doi: ...

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 ...

This course is available on the BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course ...