Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe ...

The first part of the paper deals with an infinite system of weakly coupled (this means that every equation contains derivatives of only one unknown function ...

Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Introduction to differential equations with an emphasis on engineering applications. Topics include first-order equations, higher-order linear equations with constant coefficients, and systems of ...

The Einstein field equations are a system of second order, non-linear, coupled differential equations in 4 variables. As you can imagine, solving such a system is not easy. If the system possesses a ...