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 ...

Hi all, this is my first post so please bear with me – any advice/support would be warmly welcomed. I have been doing some work on a simple RLC electronic circuit whose transfer function follows the ...

Let Φ(z) = ∑∞ 0 βjz j have radius of convergence $r (0 < r < \infty)$ and no singularities other than poles on the circle |z| = r. A complete solution is ...

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 ...

We mentioned before about the \(+ c\) term. We are now going to look at how to find the value of \(c\) when additional information is given in the question.

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 ...

When integrating simple expressions, the constant of integration, the \(+ c\) term, may remain an unknown. The value of \(c\) can be worked out when additional information is given in the question, .