This breakthrough radically changes the understanding of one of the oldest areas of mathematics, crucial to fundamental physics and economics ...

This project explores and implements a wide range of classical and advanced techniques in the field of numerical analysis and differential equations, combining symbolic computation, custom numerical ...

Discontinuous Galerkin (DG) methods represent a versatile and robust class of numerical schemes for approximating solutions to partial differential equations (PDEs). Combining elements of finite ...

Elliptic partial differential equations (PDEs) are a central pillar in the mathematical description of steady-state phenomena across physics, engineering, and applied sciences. Characterised by the ...

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 ...

SIAM Journal on Numerical Analysis, Vol. 7, No. 1 (Mar., 1970), pp. 47-66 (20 pages) Linear one step methods of a novel design are given for the numerical solution of stiff systems of ordinary ...

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

Implementação e estudo de métodos numéricos para equações diferenciais ordinárias (ex.: diferenças finitas forward, estudos de convergência e estabilidade). Exemplos de comparação entre solução ...

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 ...