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The purpose of this paper is to use the homotopy perturbation method (HPM) to obtain numerical soliton solution of the improved Boussinesq equation (IBE). The solutions are calculated in the form of a convergent power series with easily computable components.

The HPM is used to obtain numerical soliton solution of the IBE. The solutions are calculated in the form of a convergent power series with easily computable components.

The errors are obtained by using the approximate solution given by using only two iterations of the HPM. It is evident that the efficiency of this approach can be dramatically enhanced by computing further terms of approximate solution.

The numerical results presented in the paper show that only a few terms are sufficient to obtain accurate solutions.

The purpose of this paper is to concern with a reliable treatment of the (2+1)-dimensional and the (3+1)-dimensional logarithmic Boussinesq equations (BEs). The author uses the sense of the Gaussian solitary waves to determine these gaussons. The study confirms that models characterized by logarithmic nonlinearity give gaussons solitons of distinct physical structures.

The proposed technique, as presented in this work has been shown to be very efficient for solving nonlinear equations with logarithmic nonlinearity.

The (2+1) and the (3+1)-dimensional BEs were examined as well. The examined models feature interesting results in propagation of waves and fluid flow.

The paper presents a new efficient algorithm for the higher dimensional logarithmic BEs.

The work shows the effect of logarithmic nonlinearity compared to other nonlinearities where standard solitons appear in the last case.

The work will benefit audience who are willing to examine the effect of logarithmic nonlinearity.

The paper presents a new efficient algorithm for the higher dimensional logarithmic BEs.

The inverse problem of identifying the time-dependent potential coefficient along with the temperature in the fourth-order Boussinesq–Love equation (BLE) with initial and boundary conditions supplemented by mass measurement is, for the first time, numerically investigated. From the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data.

For the numerical discretization, the authors apply the Crank–Nicolson finite difference method along with the Tikhonov regularization for finding a stable and accurate approximate solution. The resulting nonlinear minimization problem is solved using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted.

The present computational results demonstrate that obtained solutions are stable and accurate.

The inverse problem presented in this paper was already showed to be locally uniquely solvable, but no numerical identification has been studied yet. Therefore, the main aim of the present work is to undertake the numerical realization. The von Neumann stability analysis is also discussed.

The paper aims to numerically solve the inverse problem of determining the time-dependent potential coefficient along with the temperature in a higher-order Boussinesq-Love equation (BLE) with initial and Neumann boundary conditions supplemented by boundary data, for the first time.

From the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, the authors apply the generalized finite difference method (GFDM) for solving the BLE along with the Tikhonov regularization to find stable and accurate numerical solutions. The regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin. The stability analysis of solution of the BLE is proved using the von Neumann method.

The present numerical results demonstrate that obtained solutions are stable and accurate.

Since noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.

The knowledge of this physical property coefficient is very important in various areas of human activity such as seismology, mineral exploration, biology, medicine, quality control of industrial products, etc. The originality lies in the insight gained by performing the numerical simulations of inversion to find the potential co-efficient on time in the BLE from noisy measurement.

The purpose of this paper is to apply the variational iterations method to solve two difference types such as the modified Boussinesq (MB) and seven‐order Sawada‐Kotara (sSK) equations and to compare this method with that obtained previously by Adomian decomposition.

The variational iteration method is used for finding the solution of the MB and sSK equations. The solution obtained is an infinite power series for appropriate initial condition. The numerical results obtain for nth approximation and compare with the known analytical solutions; the results show that an excellent approximation to the actual solution of the equations was achieved by using only three iterations.

The comparison demonstrates that the two obtained solutions are an excellent agreement. The numerical results calculated show that this method, variational iteration method, can be readily implemented to this type of nonlinear equation and excellent accuracy can be achieved. The results of variation iteration method confirm the correctness of those obtained by means of Adomian decomposition method.

The results presented in this paper show that the variational iteration method is a powerful mathematical tool for solving the MB and the sSK equations; it is also a promising method for solving other nonlinear equations.

The soil water retention curve (SWRC) and unsaturated hydraulic conductivity (UHC) are crucial indices to assess hydraulic properties of porous media that primarily depend on the particle and pore size distributions. This study aims to present a method based on the discrete element model (DEM) and the typical Arya and Paris model (AP model) to numerically predict SWRC and UHC.

First, the DEM (PFC^3D software) is used to construct the pore and particle size distributions in porous media. The number of particles is calculated according to the AP model, which can be applied to evaluate the relationship between the suction head and the moisture of porous media. Subsequently, combining critical path analysis (CPA) and fractal theory, the air entry value is applied to calculate the critical pore radius (CPR) and the critical volume fraction (CVF) for evaluating the unsaturated hydraulic conductivity.

This method is validated against the experimental results of 11 soils from the clay loam to the sand, and then the scaling parameter in the AP model and critical volume fraction value for many types of soils are presented for reference; subsequently, the gradation effect on hydraulic property of soils is analyzed. Furthermore, the calculation for unbound graded aggregate (UGA) material as a special case and a theoretical extension are provided.

The presented study provides an important insight into the relationship between the heterogeneous particle and hydraulic properties by the DEM and sheds light on the directions for future study of a method to investigate the hydraulic properties of porous media.

The purpose of this paper is to apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation, which plays a very important role in mathematical physics and engineering sciences.

The authors apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation.

Numerical results clearly indicate the reliability and efficiency of the proposed exp‐function method. The suggested algorithm is quite efficient and is practically well suited for use in these problems.

In this paper, the authors applied the exp‐function method to obtain solutions of the Fitzhugh‐Nagumo equation and show that the exp‐function method gives more realistic solutions without disturbing the basic physics of the physical problems.

The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems.

The proposed numerical technique is based on HPM to determine a heat source in the parabolic heat equation using the usual conditions. Then this shows the pertinent features of the technique in inverse problems.

Using this HPM, a rapid convergent sequence which tends to the exact solution of the problem can be obtained. And the HPM does not require the discretization of the inverse problems. So HPM is a powerful and efficient technique in finding exact and approximate solutions without dispersing the inverse problems.

The essential idea of this method is to introduce a homotopy parameter p which takes values from 0 to 1. When p=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation.

The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation.

In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives.

The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy.

The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

The purpose of this paper is to obtain accurate numerical solutions of two-dimensional (2-D) and 3-dimensional (3-D) Klein–Gordon–Schrödinger (KGS) equations.

The use of linear barycentric interpolation differentiation matrices facilitates the computation of numerical solutions both in 2-D and 3-D space within reasonable central processing unit times.

Numerical simulations corroborate the efficiency and accuracy of the proposed method.

Linear barycentric interpolation method is applied to 2-D and 3-D KGS equations for the first time, and good results are obtained.