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 ...

SIAM Journal on Applied Mathematics, Vol. 22, No. 4 (Jun., 1972), pp. 629-647 (19 pages) The two-time perturbation procedure is applied to a class of inhomogeneous initial boundary value problems for ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Vol. 10, No. 1/3, Special Conference Issue: Trento, Italy, 1984: Integrodifferential Evolution Equations and Applications (1985), pp. 73-97 (25 pages) In the last decade, the theory of abstract linear ...

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 ...

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 ...

Drichlet conditions specify the values of the dependent variables of the boundary points. Neumann conditions specify the values of the normal gradients of the boundary. Robin conditions defines a ...