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The objective of this paper is to establish a solution strategy for obtaining dual solutions, namely trivial (conventional) and nontrivial (unconventional) solutions, of coupled pore-fluid flow and chemical dissolution problems in heterogeneous porous media.

Through applying a perturbation to the pore-fluid velocity, original governing partial differential equations of a coupled pore-fluid flow and chemical dissolution problem in heterogeneous porous media are transformed into perturbed ones, which are then solved by using the semi-analytical finite element method. Through switching off and on the applied perturbation terms in the resulting perturbed governing partial differential equations, both the trivial and nontrivial solutions can be obtained for the original governing partial differential equations of the coupled pore-fluid flow and chemical dissolution problem in fluid-saturated heterogeneous porous media.

When a coupled pore-fluid flow and chemical dissolution system is in a stable state, the trivial and nontrivial solutions of the system are identical. However, if a coupled pore-fluid flow and chemical dissolution system is in an unstable state, then the trivial and nontrivial solutions of the system are totally different. This recognition can be equally used to judge whether a coupled pore-fluid flow and chemical dissolution system involving heterogeneous porous media is in a stable state or in an unstable state. The proposed solution strategy can produce dual solutions for simulating coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media.

A solution strategy is proposed to obtain the nontrivial solution, which is often overlooked in the computational simulation of coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media. The proposed solution strategy provides a useful way for understanding the underlying dynamic mechanisms of the chemical damage effect associated with the stability of structures that are built on soil foundations.

This paper aims to apply an iterative numerical method to find the numerical solution of the nonlinear non-self-adjoint singular boundary value problems that arises in the theory of epitaxial growth.

The proposed problem has multiple solutions and it is singular too; so not every technique can capture all the solutions. This study proposes to use variational iterative numerical method and compute both the solutions. The computed solutions are very close to the exact result.

It turns out that the existence or nonexistence of numerical solutions fully depends on the value of a parameter. The authors show that numerical solutions exist for small positive values of this parameter. For large positive values of the parameter, they find nonexistence of solutions. They also observe existence of solutions for negative values of the parameter and determine the range of parameter values which separates existence and nonexistence of solutions. This parameter has a clear physical meaning, as it describes the rate at which new material is deposited onto the system. This fact allows interpreting the physical significance of the results.

The authors could capture both the solutions and got accurate estimation of the parameter. This method will be a great tool to handle such types of nonlinear non-self-adjoint equations that have multiple solutions in engineering and mathematical sciences. The results in this paper will have an impact on the understanding of theoretical models of epitaxial growth in near future.

The objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.

The porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.

The direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.

Analytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

The purpose of this paper is the study of existence and multiplicity of solutions for a nonlinear discrete boundary value problems involving the p-laplacian.

The approach is based on variational methods and critical point theory.

Theorem 1.1. Theorem 1.2. Theorem 1.3. Theorem 1.4.

The paper is original and the authors think the results are new.

We build three stochastic models of garbage can processes in an organization populated by boundedly rational agents. Although short-run behavior in our models can be quite chaotic, they generate systematic, testable predictions about patterns of organizational choice. These predictions are determined, in fairly intuitive ways, by the degree of preference conflict among agents in the organization, by their patterns of attention, and by their tendencies to make errors. We also show that nontrivial temporal orders can arise endogenously in one of our models, but only when some form of intentional order, based on agents’ preferences, is also present.

The main purpose of this paper is to develop two efficient and accurate numerical analytical methods for engineering computation of natural sloshing frequencies and modes i the case of truncated circular conical tanks.

The numerical‐analytical methods are based on a Ritz Treftz variational scheme with two distinct analytical harmonic functional bases.

Comparative numerical analysis detects the limit of applicability of variational methods in terms of the semi‐apex angle and the ratio between radii of the mean free surface and the circular bottom. The limits are caused by different analytical properties of the employed functional bases. However, parallel use of two or more bases makes it possible to give an accurate approximation of the lower natural frequencies for relevant tanks. For V‐shaped tanks, dependencies of the lowest natural frequency versus the semi‐apex angle and the liquid depth are described.

The methods provide the natural sloshing frequencies for V‐shaped tanks that are valuable for designing elevated containers in seismic areas. Approximate natural modes can be used in derivations of nonlinear modal systems, which describe a resonant coupling with structural vibrations.

Although variational methods have been widely used for computing the natural sloshing frequencies, this paper presents their application for truncated conical tanks for the first time. An original point is the use of two distinct functional bases.

The purpose of this study is to investigate the problem of fault accommodation in bilinear dynamic systems.

Solution to this problem is related to constructing the control law which provides full decoupling with respect to the fault effects. The so-called logic-dynamic approach will be used to solve this problem. The main steps of this approach are: replacing the initial bilinear system by certain linear one, solving the problem under consideration for this linear system by well-known linear methods with some restrictions, taking into account the bilinear term to correct the obtained linear solution.

Existing conditions of the fault accommodation problem in a form of rank equalities and inequalities are formulated. Calculating relations for the control law and the auxiliary systems are given.

The suggested method allows determining such a control law that preserves the main performances of the system in the faulty case, while the minor performances may degrade.

The main advantage of the logic-dynamic approach is a possibility to solve the problem of fault accommodation for nonlinear systems by linear methods without decreasing the main properties of the obtained solution.

Because of the unrealistic demand of computer resources in terms of memory and CPU times for the direct numerical simulation of practical peen forming processes, a two‐stage combined finite/discrete element and explicit/implicit solution strategy is proposed in this paper. The procedure involves, at the first stage, the identification of the residual stress/strain profile under particular peening conditions by employing the combined finite/discrete approach on a small scale sample problem, and then at the second stage, the application of this profile to the entire workpiece to obtain the final deformation and stress distribution using an implicit static analysis. The motivation behind the simulation strategy and the relevant computational and implementation issues are discussed. The numerical example demonstrates the ability of the proposed scheme to simulate a peen forming process.

The aim of this paper is to study the global behavior of a higher order nonlinear difference equation.

The character of semicycles, periodicity, global stability and boundedness of positive solutions of the mentioned difference equation are investigated.

It is deduced that, when q<1, then the positive equilibrium of this equation is globally asymptotically stable and, when q>1, then this difference equation possesses unbounded solutions.

The paper investigates some of the characteristics of nonlinear difference equations.

The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. This method, which is based on Padé-approximation and homotopy–Padé technique, is applied to a model of magnetohydrodynamic Falkner–Skan flow as well. These examples indicate that the method can be successfully applied to solve nonlinear differential equations arising in science and engineering.

Homotopy–Padé method.

The main focus of the paper is on the prediction of the multiplicity of the solutions, however we have calculated multiple (dual) solutions of the model problem namely, mixed convection heat transfer in a porous medium.

The authors conjecture here that the combination of traditional–Pade and Hankel–Pade generates a useful procedure to predict multiple solutions and to calculate prescribed parameter with acceptable accuracy as well. Validation of this conjecture for other further examples is a challenging research opportunity.

Dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain.

In this study, the authors are using two modified methods.