Thus, this is an example of using the method of matched asymptotic expansions to satisfy the given initial condition by the long-distance approximation of the solution to a nonsingular partial ...

Waveguide-based structures can solve partial differential equations by mimicking elements in standard electronic circuits. This novel approach, developed by researchers at Newcastle University in the ...

Facebook researchers built a new neural network that can solve complex mathematical equations, even those dealing with calculus. Here's how it works.

Techniques for solving these for various initial and boundary value problems on bounded and unbounded domains, using eigenfunction expansions (separation of variables, and elementary Fourier series), ...

A. M. Stuart, A. R. Humphries, Model Problems in Numerical Stability Theory for Initial Value Problems, SIAM Review, Vol. 36, No. 2 (Jun., 1994), pp. 226-257 ...

- Initial value problem: PDE in question describes time evolution, i.e., the initial space-distribution id given; the goal is to find how the dependent variable propagates in time. Example: The ...

Inverse Problem So solving the initial value problem with data given at time t=0 works. We now turn to the backward (inverse) problem: Assume that we measure temperature u (x,T) at time t=T>0. Can we ...