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 ...

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 ...

Time-domain finite-difference (TDFD) method is the most dominant approach for seismic wavefield simulation. Due to the memory and computational cost of the computer, finite-difference (FD) simulations ...

A superexponentially convergent method for solving the Sturm-Liouville problem with Legendre's differential operator is given. The presented method (called the FD-method) is based on the coefficient ...