The field of numerical methods for complex systems is moving towards the development of more efficient and accurate algorithms for solving various types of equations, including nonlocal Poisson problems, viscous Burgers' equations, and Vlasov equations. Researchers are focusing on creating high-order methods, such as finite difference schemes and finite element methods, that can handle nonlinear problems and provide optimal convergence rates. Additionally, there is a growing interest in developing methods that can efficiently simulate complex systems, such as those involving contact mechanics, magnetoelastic effects, and multiscale problems. Noteworthy papers in this area include the development of a high-order weighted positive and flux conservative method for the Vlasov equation, and the creation of a decoupled, unconditionally stable, and second-order integrator for the Landau-Lifshitz-Gilbert equation with magnetoelastic effects. These advancements have the potential to significantly impact various fields, including physics, engineering, and materials science.
Numerical Methods for Complex Systems
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A Matlab code for analysis and topology optimization with Third Medium Contact
Finite Difference Method for Global Stabilization of the Viscous Burgers' Equation with Nonlinear Neumann Boundary Feedback Control
Asymptotic Compatibility of the Approximate-Ball Finite Element Method for 2D Nonlocal Poisson Problem with Neumann Boundary Conditions
Error analysis of an acceleration corrected diffusion approximation of Langevin dynamics with background flow
A high-order weighted positive and flux conservative method for the Vlasov equation
A note on the central-upwind scheme for nonlocal conservation laws
Convergence of long-time stable variable-step arbitrary order ETD-MS scheme for gradient flows with Lipschitz nonlinearity
A Two-Stage Fourth-Order Implicit Scheme for Stiff problems
A decoupled, unconditionally stable and second-order integrator for the Landau--Lifshitz--Gilbert equation with magnetoelastic effects
Error estimates for semi-Lagrangian schemes with higher-order interpolation for conservation laws with dispersive terms
An efficient fully decoupled finite element method with second-order accuracy for the micropolar Rayleigh-Benard convection system
Relaxation Schemes for Flows in Networks: Application to Shallow Water and Blood Flow Equations
Convergence analysis of a Crank-Nicolson scheme for strongly magnetized plasmas
From Memory Model to CPU Time: Exponential Integrators for Advection-Dominated Problems
Iterative Contact-resolving Hybrid Methods for Multiscale Contact Mechanics
Recent advances in the numerical solution of multi-order fractional differential equations
Construction of the Nearest Nonnegative Hankel Matrix for a Prescribed Eigenpair
A High-Order Discretization Scheme for Surface Integral Equations for Analyzing the Electroencephalography Forward Problem