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 ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

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 ...

We prove the existence of inertial manifolds for partial functional differential equation du(t)dt+Au(t)=F(t)ut+g(t,ut) under the conditions that the partial differential operator 𝐴 is positive such ...

Fuzzy Zoeller, two-time major champion haunted by racist joke about Tiger Woods, dies at 74 Sea lion surprises swimmers near Victoria, B.C. Dick Van Dyke, 99, names the two things to avoid to live a ...

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...