The ubiquity of semilinear parabolic equations is clear from their numerous applications ranging from physics and biology to materials and social scie......
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged o......
Polynomial approximations constructed using a least-squares approach form a ubiquitous technique in numerical computation. One of the simplest ways to......
Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades an important research effort h......
Whether the three-dimensional incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most chal......
Multiplicative and additive D-stability, diagonal stability, Schur D-stability, and H-stability are classical concepts which arise in studying linear ......
We propose a new numerical technique to deal with nonlinear terms in gradient flows. By introducing a scalar auxiliary variable (SAV), we construct ef......
The main purpose of this paper is to present some of our recent results about the second-order necessary conditions for stochastic optimal controls wi......
