The numerical solution to boundary differential problems is a crucial task in modern applied mathematics. Usually, implicit integration methods are applied to solve this class of problems due to their high numerical stability and convergence. The kno...
Numerical stability is a critical property of ODE solvers that must be taken into account when choosing a numerical method for solving a certain initial value problem. However, conventional approaches to evaluating numerical stability are not directl...
The viscoplastic model proposed by Vermeer and Neher in 1999 is still currently used in the oil and gas industry for subsidence modeling, to predict the deformation of the ground surface induced by hydrocarbon withdrawal from underground reservoirs....
Implicit integration factor (IIF) methods were developed for solving time-dependent stiff partial differential equations (PDEs) in literature. In [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368–388], IIF methods are designed to eff...
Rayleigh damping is proportional to the combination of the structural mass matrix and stiffness matrix and is widely used in structural seismic analysis. The accuracy of seismic analysis of nuclear power structures directly depends on the value of th...
This paper is concerned with a class of implicit-type coupled system with integral boundary conditions involving Caputo fractional derivatives. First, the existence result of solutions for the considered system is obtained by means of topological deg...
The main goal of this study is to demonstrate an existence result of a coupled implicit Riemann-Liouville fractional integral equation. First, we prove a new fixed point theorem in spaces with an extended norm structure. That theorem generalized Darb...
The computation of the minimum distance between a point and a planar implicit curve is a very important problem in geometric modeling and graphics. An integrated hybrid second order algorithm to facilitate the computation is presented. The proofs ind...
In this paper, a family of high-order linearly implicit exponential integrators conservative schemes is constructed for solving the multi-dimensional nonlinear fractional Schrödinger equation. By virtue of the Lawson transformation and the gener...
The accuracy, stability and computational efficiency of numerical methods on central processing units (CPUs) for the depth-averaged shallow water equations were well covered in the literature. A large number of these methods were already developed an...
Discontinuous deformation analysis (DDA) is a discontinuum-based and implicit method for investigating the deformational behavior of block systems. The constant acceleration integration (CAI) scheme characterized by unconditional stability is employe...
Geophysical flows are characterized by rapid rotation. Simulating these flows requires small timesteps to achieve stability and accuracy. Numerical stability can be greatly improved by the implicit integration of the terms that are most responsible f...
This study delves into the effectiveness of two time integration techniques, namely the adaptive implicit–explicit (imp–exp) and explicit–explicit (exp–exp) methods, which stand as efficient formulations for tackling intricate...
Multistep integration methods are widespread in the simulation of high-dimensional dynamical systems due to their low computational costs. However, the stability of these methods decreases with the increase of the accuracy order, so there is a known...
A fully implicit stress integration algorithm is developed for the distortional hardening model, namely the e−HAH model, capable of simulating cross−hardening/softening under orthogonal loading path changes. The implicit algorithm solves a complete s...
In this paper, we introduce a generalized
A time integration scheme based on semi-Lagrangian advection and Laplace transform adjustment has been implemented in a baroclinic primitive equation model. The semi-Lagrangian scheme makes it possible to use large time steps. However, errors arising...
Multistep methods for the numerical solution of ordinary differential equations are an important class of applied mathematical techniques. This paper is motivated by recently reported advances in semi-implicit numerical integration methods, multistep...
Composition is a powerful and simple approach for obtaining numerical integration methods of high accuracy order while preserving the geometric properties of a basic integrator. Adaptive step size control allows one to significantly increase the perf...
Developing a high-quality, real-time, dense visual SLAM system poses a significant challenge in the field of computer vision. NeRF introduces neural implicit representation, marking a notable advancement in visual SLAM research. However, existing neu...
Discontinuous Galerkin (DG) method is a popular high-order accurate method for solving unsteady convection-dominated problems. After spatially discretizing the problem with the DG method, a time integration scheme is necessary for evolving the result...
Multi-component flow problems are typical of many technological and engineering applications. In this work, we propose an implicit high-order discontinuous Galerkin discretization of the variable density incompressible (VDI) flow model for the simula...
This paper implemented the Barcelona basic model (BBM) into the OpenGeoSys (OGS) platform for numerical modeling of the coupled hydro-mechanical (HM) behavior of unsaturated soil. Within the implicit integration approach in the OGS, the integration r...
An unsaturated soil constitutive model considering the influence of microscopic pore structure can more accurately describe the hydraulic–mechanical behavior of unsaturated soil, but its numerical implementation is more complicated. Based on the full...
In this work, a high-order modal discontinuous Galerkin (dG) method is employed to solve the Euler equations using entropy variables. Entropy conservation and stability are ensured at the spatial semi-discrete level through entropy-conserving/stable...
Eye-movement research on implicit prosody has found effects of lexical stress on syntactic ambiguity resolution, suggesting that metrical well-formedness constraints interact with syntactic category assignment. Building on these findings, the present...
This research paper focuses on investigating the solvability of a constrained problem involving a nonlinear delay functional equation subject to a quadratic functional integral constraint, in two significant cases: firstly, the existence of nondecrea...
A numerical stability region is a valuable tool for estimating the practical applicability of numerical methods and comparing them in terms of stability. However, only a little information can be obtained from the stability regions when their shape i...
In this paper, the nonlinear bending of the slender flexible cable connected to floating offshore energy platforms is considered. The aim is to find accurate values for the bending stress in the catenaries that lead to fatigue and short lifetime. A n...
The complex structure of a diesel engine crankshaft, combined with diverse and dynamically changing loads, leads to the interaction of torsional, bending, and longitudinal vibrations. These complexities present challenges in achieving comprehensive a...
In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the suffic...
Fullerenes, particularly C60, exhibit unique properties that make them promising candidates for various applications, including drug delivery and nanomedicine. However, their interactions with biomolecules, especially proteins, remain not fully under...
Exponential integrator (EI) method based on Krylov subspace approximation is a promising method for large-scale transient circuit simulation. However, it suffers from the singularity problem and consumes large subspace dimensions for stiff circuits w...
This paper investigates the existence and uniqueness of implicit solutions in a coupled symmetry system of hybrid fractional order differential equations, along with hybrid integral boundary conditions in Banach Algebras. The methodology centers on a...
This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and...
In this paper, an implicit difference scheme is proposed and analyzed for a class of nonlinear fourth-order equations with the multi-term Riemann–Liouvile (R–L) fractional integral kernels. For the nonlinear convection term, we handle imp...
In image-guided radiation therapy (IGRT), deformable image registration between computed tomography (CT) and cone beam computed tomography (CBCT) images remain challenging due to the computational cost of iterative algorithms and the data dependence...
Semi-implicit multistep methods are an efficient tool for solving large-scale ODE systems. This recently emerged technique is based on modified Adams–Bashforth–Moulton (ABM) methods. In this paper, we introduce new semi-explicit and semi-...
In this paper, we introduce and thoroughly examine new generalized
We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.
The rapid growth of the global population and associated increases in resource consumption have accelerated environmental degradation, making sustainable design and construction processes increasingly essential. The construction sector holds signific...
Numerical techniques for approximate solution of a system of reaction-diffusion-convection partial differential equations modeling the evolution of temperature and fuel density in a wildfire are proposed. These schemes combine linearly implicit-expli...
The propagation of a forest fire can be described by a convection–diffusion–reaction problem in two spatial dimensions, where the unknowns are the local temperature and the portion of fuel consumed as functions of spatial position and tim...
We introduce firm solar forecasts as a strategy to operate optimally overbuilt solar power plants in conjunction with optimally sized storage systems so as to make up for any power prediction errors, and hence entirely remove load balancing uncertain...
In this paper, we introduce the matrix Mittag–Leffler function, which is a generalization of the multivariate Mittag–Leffler function, in order to investigate the uniqueness of the solutions to a fractional nonlinear partial integro-diffe...
This study addresses the limitations of and the common challenges faced by one-dimensional river-routing methods in hydrological models, including the National Water Model (NWM), in accurately representing coastal regions. We developed a two-way coup...
Developing new and efficient numerical integration techniques is of great importance in applied mathematics and computer science. Among the variety of available methods, multistep ODE solvers are broadly used in simulation software. Recently, semi-im...
This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system, different from the generally accepted approach based on the method of splitting according to physical processes. A combined expli...
The objective of the pansharpening task is to integrate multispectral (MS) images with low spatial resolution (LR) and to integrate panchromatic (PAN) images with high spatial resolution (HR) to generate HRMS images. Recently, deep learning-based pan...
In this paper, we study the existence and uniqueness of solutions for a coupled implicit system involving
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