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 ...

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

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 ...

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 ...

A Russian mathematician has developed a new method for analyzing a class of equations that underpin models in physics and ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Many years ago while taking an electrical engineering class at the University of the Philippines in Diliman, I was thoroughly impressed by my professor, Bartolome Blanco, who solved a differential ...