Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

We show that any entire solution of an essentially nonlinear first-order partial differential equation in two variables must be linear. Journal Information This monthly journal, begun in 1950, is ...

An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem y' = Ay are inside this region, the numerical ...

First-order systems are those which can be described by first-order differential equations. A common example is the RC circuit. You will need Adobe Acrobat Reader to ...

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 ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...