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The paper is devoted to the study of the backward behavior of solutions of the initial boundary value problem for the chevron pattern equations under homogeneous Dirichlet’s boundary conditions. We prove that, as t → ∞, the asymptotic behavior of ...

In this work, the penalty method is studied for the mixed Stokes–Darcy problem, motivated by the penalty method applied to Stokes equation. This work first proposes the penalty Stokes–Darcy model at the continuous level. Then we prove that the ...

• A penalty method is proposed for solving the mixed Stokes–Darcy problem.
• We propose the penalty model at the continuous level and prove that the solution of the penalty model strongly convergences to the solution of the original model ...

In this paper, we study a heat transfer scenario in Darcy–Forchheimer porous media with variable density. The block-centered finite difference method is applied to discretize the non-isothermal flow equations governing the system. Specifically, ...

This paper presents an efficient numerical method for solving nonlinear stochastic delay integro-differential equations based on block pulse functions. Firstly, the equation is transformed into an algebraic system by the integral delay operator ...

In this article, we present an error estimation in the L 2 norm referring to three wave models with variable coefficients, supplemented with initial and boundary conditions. The first two models are nonlinear wave equations with Dirichlet, ...

• We established two key theorems with error estimation in the L 2 norm for approximation solutions of three wave models.
• Two nonlinear wave equations with Dirichlet, Acoustics, and nonlinear dissipative Impenetrability boundary ...

This study investigated the deformation-dependent earth pressure evolution on the periphery of the grid wall-pattern foundation fully embedded into soft ground. The numerical modelling was performed using the embedded Modified Cam Clay ...

• Earth pressure on cement-based deep improved soft clay.
• Determination of the coefficient of earth pressure along the depth of the improved soft clay.
• Numerical modelling and post-processing using machine learning and GeneXproTools.

A reverse engineering approach is taken to develop efficient numerical techniques for solving nonlinear ODEs through the numerical solution of a particular problem in engineering. The problem is the dynamic analysis of a mechanical system under a ...

• An efficient two-derivative time integration scheme is developed for solving IVPs.
• Four levels of weighting rules are presented for this integrator.
• A series of high-precision Hermite interpolators are extended to collaborate with ...

Standard Galerkin methods often perform poorly for problems with low diffusion. In particular for purely convective transport, least-squares (LS) formulations provide a good alternative. While spatial stability is relatively straightforward in a ...

In this paper, the cost function of a single-server queueing system with Poisson input stream and Erlang-k service time will be analyzed. Treated as a function of the traffic intensity ρ, with respect to some known constants, we will show that ...

• A cost function is formed for single-server queueing system with Poisson input stream and Erlang-k service time.
• Stationary points of the proposed cost function are solutions of fourth-degree polynomial equation with real coefficients.

This article is intended to present a qualitative and numerical analysis of well-posedness and boundary stabilization problems of the well-known Korteweg-de Vries-Burgers equation. Assuming that the boundary control is of memory type, the history ...

In this paper, a two-grid characteristic block-centered finite difference method is developed for solving a nonlinear Darcy-Forchheimer slightly compressible miscible displacement problem in porous media. The method is proposed for solving the ...

This paper deals with stability of classical Runge–Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [13] and used in [14] for the time integration of nonlinear evolution PDEs, the stability of ...

In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and $L^1$ data. To deal with the non-coercive character of the equation and the low regularity of the ...

A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this paper ...

Recycled aggregate concrete-filled steel tube (RACFST) columns are widely used in engineering practice due to the advantages of avoiding steel tubes corrosion and reducing self-weight of the elements. A three-dimensional solid numerical modeling was ...

Most of the existing domestic and international studies on the external blast response of the wall face take the physical distance between the wall and the source as the research distance, neglecting the role of the blast equivalent in its development ...

Multi-physics are widely studied and used in numerical analysis and simulation. Physics-based splitting methods are introduced, in which different methods are applied to solve each individual aspect of a physical system in multiple steps. The ...

• Numerical methods used for the estimation of the RMS.
• Simpson's 1/3 rule and Simpson's 3/8 rule modified for the purpose of general application.
• Modified Simpson's rules do not necessitate more complex mathematical calculations ...

This paper demonstrates that direct changes in the algorithm for the estimation of the root mean square value of a voltage signal of an arbitrary waveform can lead to improved performances and lower measurement uncertainty of commercially ...

The integrity of plate structures in numerous facilities and vehicles is essential for ensuring safety. Guided wave testing is a prominent non-destructive testing (NDT) technique, especially for wide plate or long pipe structures. It can be ...

The ordinary differential equation (ODE) models of optimization methods allow for concise proofs of convergence rates through discussions based on Lyapunov functions. The weak discrete gradient (wDG) framework discretizes ODEs while preserving the ...