The past several decades have seen significant development in the design and numerical
analysis of particle methods for approximating solutions of PDEs. In these methods, a …

The purpose of this paper is to provide global existence and uniqueness results for a family
of fluid transport equations by establishing convergence results for the particle method …

In this paper, we study simple splines on a Riemannian manifold $ Q $ from the point of view
of the Pontryagin maximum principle (PMP) in optimal control theory. The control problem …

The purpose of this paper is to study the dynamics of the interaction among a special class
of solutions of the one-dimensional Camassa–Holm equation. The equation yields soliton …

Chemotaxis systems play a crucial role in modeling the dynamics of bacterial and cellular
behaviors, including propagation, aggregation, and pattern formation, all under the influence …

The purpose of this paper is to develop and test novel invariant-preserving finite difference
schemes for both the Camassa-Holm (CH) equation and one of its 2-component …

We study the two-component Camassa-Holm (2CH) equations as a model for the long time
water wave propagation. Compared with the classical Saint-Venant system, it has the …

We present an efficient landmark shooting algorithm for template matching and its
applications. The novelties of the algorithm include the use of a constant matrix to update the …

We present a new structure‐preserving numerical scheme for solving the Euler‐Poincaré
Differential (EPDiff) equation on arbitrary triangle meshes. Unlike existing techniques, our …

The purpose of this paper is to establish a new method for proving the convergence of the
particle method applied to the Camassa-Holm (CH) equation. The CH equation is a strongly …