Abstract: Adversarial attacks craft adversarial examples (AEs) to fool convolution neural networks. The mainstream gradient-based attacks, based on first-order optimization methods, encounter ...

The problem of the region of stability of the fourth order-Runge-Kutta method for the solution of systems of differential equations is studied. This region can be characterized by means of linear ...

YASK--Yet Another Stencil Kit: a domain-specific language and framework to create high-performance stencil code for implementing finite-difference methods and similar applications.

"- I want to implement and illustrate the [Runge-Kutta method](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) (actually, different variants), in the ...

Abstract: Explicit Runge–Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial ...

Institute of Mathematics and Computer Science, University of S?o Paulo, S?o Carlos, Brazil. Institute of Physics, University of S?o Paulo, S?o Paulo, Brazil. The kinetic electron trapping process in a ...

In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta ...

Explicit Runge-Kutta methods (RKMs) are among the most popular classes of formulas for the approximate numerical integration of nonstiff, initial value problems. However, high-order Runge-Kutta ...