Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Annals of Mathematics, Vol. 40, No. 4 (Oct., 1939), pp. 862-891 (30 pages) ...

If today's college students could find a way to get their hands on a copy of Facebook's latest neural network, they could cheat all the way through Calc 3. They could even solve the differential ...

The Annals of Applied Probability, Vol. 28, No. 3 (June 2018), pp. 1943-1976 (34 pages) The initial-boundary value problem for the heat equation is solved by using an algorithm based on a random walk ...

Approximate solutions to more complex equations can be found using a process called iteration. Iteration means repeatedly carrying out a process. To solve an equation using iteration, start with an ...

We examine a heat problem in 1D. Assume that a rod with given temperature distribution u_0(x) is cooled to temperature 0 on the exteriors at 0 and pi. Assume that u(x,t) for the Temperature at point x ...