Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...

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 ...

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 ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

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 ...