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

There are many numerical methods used for the integration of the Equation (2); the Runge-Kutta method has been designed to solve first-order differential equations (Es-hagh 2005).This method (the R-K ...

This repository contains a Python implementation for solving ordinary differential equations (ODEs) using various numerical methods, including the Euler method, Heun's method, the Midpoint method, and ...

D.D. Olesky, P. van den Driessche and J.H. Verner, Graphs with the same determinant as a complete graph, Linear Algebra and its Applications 312 (2000), ... J.H. Verner, Selecting a Runge--Kutta ...

We provide examples of such methods up to PEP order six, and test them on Hamiltonian ODE and PDE systems. We find that these methods behave similarly to exactly energy-conservative methods over ...

We compare our semi-analytical results with numerical solutions obtained using the Runge-Kutta 4th-order (RK-4) method. Furthermore, we analyze the model’s behaviour and dynamics by changing the ...

The class of linear multistep methods (2) becomes a spe-cial class of the multistep collocation method when s = t + 1 and x ∈ [x 0, b] which can also be solved simultaneously to obtain ...