The present paper describes implementation details of a new implementation of a BDF solver within MATLAB R . It is tuned to be most efficient when applied as a solver within FEMLAB R . The present code aims at a predictable and efficient performance for index-2 differential-algebraic equations arising within the method of lines. The main novelty is the consequent implementation of a predictive ...

This is a survey of essentially normal operators and related developments. There is an overview of Weyl–von Neumann theorems about expressing normal operators as diagonal plus compact operators. Then we consider the Brown–Douglas–Fillmore theorem classifying essentially normal operators. Finally we discuss almost commuting matrices, and how they were used to obtain two other proofs of the BDF t...

I describe an adaptive h-reenement method for solving reaction-diiusion systems in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for irregular grids are used...

Abstract Mountain forest ecosystems play an important role in global carbon sequestration and may respond differently to variations climate. The timely accurate assessment of the factors (abiotic biotic) that affect types will improve our understanding ecological mechanisms underlying stock dynamics. Here, we used linear mixed effect models assess impact abiotic biotic on rate net tree C accumu...

The $p$-step backwards difference formula (BDF) for solving the system of ODEs can result in a kind all-at-once linear systems, which are solved via parallel-in-time preconditioned Krylov subspace solvers (see McDonald, Pestana, and Wathen [SIAM J. Sci. Comput., 40(2) (2018): A1012-A1033] Lin Ng [arXiv:2002.01108, 17 pages]. However, these studies ignored that BDF ($p\geq 2$) is not selfstartin...

A chemical kinetics algorithm is presented for geochemical applications. The algorithm is capable of handling both equilibriumand kinetically-controlled reactions in multiphase systems. The ordinary differential equations (ODEs) are solved using an implicit multistep backward differentiation formula (BDF) algorithm to ensure efficiency and stability when integrating stiff ODEs. An adaptive cont...

Concrete cracks have always been the focus of research because serious damage they cause to structures. With updating hardware and algorithms, detection concrete structure surface based on computer vision has received extensive attention. This paper proposes an improved algorithm open-source model Deeplabv3+ names it BDF according optimization strategy used. first replaces original backbone Xce...