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math.NA2025
Fourth-Order Compact FDMs for Steady and Time-Dependent Nonlinear Convection-Diffusion Equations
Qiwei Feng, Catalin Trenchea
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonline…
math.NA2025
Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables
Zhen Yao, Catalin Trenchea, Wenlong Pei
Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm…
math.NA2025
A High-Accuracy Symplectic Scheme for a nonlinear transport problem
Farjana Siddiqua, Catalin Trenchea
We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process.We prove stability and error estimates for both c…