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 ...

Finite element methods (FEM) have emerged as a versatile and robust framework for the numerical simulation of evolving partial differential equations (PDEs). These methods discretise complex ...

Abstract Waveform relaxation methods are decoupling or splitting methods for large scale ordinary differential equations. In this paper, we apply the methods directly to semi-linear parabolic partial ...

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 ...

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 ...

Learn how to solve differential equations using Euler and Runge-Kutta 4 methods! This tutorial compares both techniques, explaining accuracy, step size, and practical applications for physics and ...

Abstract: In this study, we presented numerical methods for determining the minimum energy state among three dynamic systems governed by a class of integro-differential equation with weakly singular ...

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