Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

Boundary value problems in differential equations constitute a fundamental area of study in mathematical science, where solutions to differential equations are sought under prescribed conditions ...

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 strong predictor-corrector method for the numerical solution of stochastic delay differential equations (SDDEs) of Itô-type. The method is proved to be mean-square convergent of ...

We consider the numerical approximation of a semilinear fractional order evolution equation involving a Caputo derivative in time of order α ϵ (0,1). Assuming a Lipschitz continuous nonlinear source ...

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 ...