The problem of solving sparse Systems of Linear Algebraic Equations (SLAE) by parallel Monte Carlo numerical methods is considered. The almost optimal Monte Carlo algorithms are pr...
This paper develops a nested iteration algorithm to solve time-dependent nonlinear systems of partial differential equations. For each time step, Newton’s method is used to form...
J. H. Adler, Thomas A. Manteuffel, Stephen F. McCo...
Frequently, the computation of derivatives for optimizing time-dependent problems is based on the integration of the adjoint differential equation. For this purpose, the knowledge...
Abstract: Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time ...
Brian P. Sprouse, Christopher L. MacDonald, Gabrie...
As Field Programmable Gate Arrays (FPGAs) have reached capacities beyond millions of equivalent gates, it becomes possible to accelerate floating-point scientific computing applica...