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math.NA2026
A single LU~factorization approach to model reduction for linear system families with a quadratic matrix pencil
Mikhail A. Botchev, Leonid Knizhnerman, Nikolai L. Zamarashkin +1
To solve a family of large linear systems where the system matrix depends on the family parameter quadratically, we propose a new solution approach. Our method employs the derivati…
math.NA2026
Are implicit schemes needed in adaptive time stepping for PDEs?
Mikhail A. Botchev
Implicit time integration is the standard way to overcome the tight CFL time step restriction when solving nonstationary PDEs numerically. However, within an adaptive time accurate…