Spectral methods are becoming increasingly prevalent in solving time-varying partial differential equations due to their fast convergence properties.
Based on this idea, we extended the proposed algorithm for selecting a good value of shape parameter c in solving time-dependent partial differential equations.
It is interesting to note that research on solving fractional PDEs has attracted much attention recently, and there have been some new developments especially in solving time-fractional PDEs of the Fan sub-equations method (e.g., [25, 26]).
The designed order of accuracy for temporal discretization scheme is validate and the present implicit solver shows the superior performance by allowing quite large time step to be used in solving time-implicit systems.
Anytime algorithms offer a tradeoff between solution quality and computation time that has proved useful in solving time-critical problems such as planning and scheduling, belief network evaluation, and information gathering.
Collective search for people and information has tremendously benefited from emerging communication technologies that leverage the wisdom of the crowds, and has been increasingly influential in solving time-critical tasks such as the DARPA Network Challenge DNCC, also known as the Red Balloon Challenge).
We confirm this reduction in solve time with numerical experiments.
However, we found very large variance in the puzzle solving time for hash function-based puzzles.
The variance in the puzzle solving time needs to be minimized to avoid such a problem.
In this paper we propose a numerical method that can be used in solving the time-dependent nonlinear Schrödinger equation in both real and imaginary times.
Computer simulation results further demonstrate the superior performance of the ZNN model in solving the time-varying linear matrix equation compared with the conventional GNN model.
