Rethinking Heun's modified Euler method. Previously, we derived Heun's modified Euler method based on numerical integration via the trapezoidal rule. We now take a different viewpoint that leads to ...
This report provides a detailed examination of Runge-Kutta methods, which are widely used numerical techniques for solving differential equations. The objective is to offer a deep understanding of ...
In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the ...
SIAM Journal on Numerical Analysis, Vol. 31, No. 4 (Aug., 1994), pp. 1147-1168 (22 pages) This work analyzes the integration of initial value problems for stiff systems of ordinary differential ...
Abstract: Adversarial attacks craft adversarial examples (AEs) to fool convolution neural networks. The mainstream gradient-based attacks, based on first-order optimization methods, encounter ...
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