Title: Trace ratio multilinear dimensionaly reduction methods in data science

Abstract

Title: A Bi-Nonlinear Volterra Integral Equation Approach to Earthquake Modeling

Abstract: Classical seismic models often rely on partial differential equations, which are prone to numerical instabilities when simulating complex tectonic interactions. In this study, we propose a novel approach using bi-nonlinear Volterra integral equations to model earthquake phenomena with greater accuracy and stability. Unlike previous models that assume a constant friction force, our formulation incorporates a non-constant Coulomb-type resistance, ensuring a more realistic representation of seismic activity. We first establish the existence and uniqueness of the solution to our model before implementing a numerical scheme based on the Nystrom method. Our results demonstrate that this integral approach not only improves numerical stability but also aligns more closely with observed seismic behaviors, particularly in eliminating artificial oscillations introduced by the constant friction and the numerical approximation. This study highlights the advantages of fractional and integral-based modeling techniques in overcoming computational challenges in earthquake simulations.