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...

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...

High-order semi-implicit Picard integral deferred correction (SIPIDC) methods have previously been proposed for the time-integration of partial differential equations with two or more disparate time scales. The SIPIDC methods studied to date compute a high-order approximation by first computing a provisional solution with a first-order semi-implicit method and then using a similar semiimplicit ...

Oleaginous microalgae are one of the promising resource of nonedible biodiesel fuel (BDF) feed stock alternatives. Now a challenge task is the decrease of the long-chain polyunsaturated fatty acids (PUFAs) content affecting on the BDF oxidative stability by using gene manipulation techniques. However, only the limited knowledge has been available concerning the fatty acid and PUFA synthesis pat...

A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a hi...

This study introduces, analyses and implements space-time discretizations of two-dimensional active dissipative partial differential equations such as the Topper–Kawahara equation; this is the two-dimensional extension of the dispersively modified Kuramoto–Sivashinsky equation found in falling film hydrodynamics. The spatially periodic initial value problem is considered as the size of the peri...