A mathematician has developed new methods for the numerical solution of ordinary differential equations. These so-called multirate methods are highly efficient for large systems, where some components ...

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 ...

We present a method to find fundamental solutions for a class of partial differential equations that often arise in fluid dynamics and in transport problems. The method is elementary in the sense that ...

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 ...