The field of numerical methods for complex systems is rapidly evolving, with a focus on developing innovative and efficient algorithms for solving various types of equations. Recent developments have centered around creating pressure-robust and parameter-free methods, as well as energy-stable schemes for computing ground states and simulating dynamics. Noteworthy papers in this area include: An Efficient Unconditionally Energy-Stable Numerical Scheme for Bose--Einstein Condensate, which proposes a novel gradient flow approach with a Lagrange multiplier and free energy dissipation. The paper Unconditional optimal-order error estimates of linear relaxation compact difference scheme for the coupled nonlinear Schr"odinger system presents a linear, decoupled, mass- and energy-conserving numerical scheme with optimal-order error estimates.
Advances in Numerical Methods for Complex Systems
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A pressure-robust and parameter-free enriched Galerkin method for the Navier-Stokes equations of rotational form
An Efficient Unconditionally Energy-Stable Numerical Scheme for Bose--Einstein Condensate
Unconditional optimal-order error estimates of linear relaxation compact difference scheme for the coupled nonlinear Schr\"odinger system
On Boundedness of Quadratic Dynamics with Energy-Preserving Nonlinearity
An energy cascade finite volume scheme for a mixed 3- and 4-wave kinetic equation arising from the theory of finite-temperature trapped Bose gases
Improved $L^2$-error estimates for the wave equation discretized using hybrid nonconforming methods on simplicial meshes
A $\mu$-Analysis and Synthesis Framework for Partial Integral Equations using IQCs
Adaptive Ch Method with Local Coupled Multiquadrics for Solving Partial Differential Equations
An efficient fully explicit scheme for stochastic Navier-Stokes equations driven by multiplicative noise