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This paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.

The governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.

The results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.

The results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.

This paper aims to suggest a novel modified Laplace decomposition method (MLDM) for MHD flow over a non-linear stretching sheet with slip condition by suitable choice of an initial solution.

The governing partial differential equations are converted into dimensionless non-linear ordinary differential equation by similarity transformation, which is solved by MLDM. The method is based on the application of Laplace transform to boundary layers in fluid mechanics. The non-linear term can be easily handled by the use of He's polynomials.

The series solution of the MHD flow of an incompressible viscous fluid over a non-linear stretching sheet subject to slip condition is obtained. An excellent agreement between the MLDM and HPM is achieved. Convergence of the obtained series solution is properly checked by using the ratio test.

Stretching surface is an important type of flow occurring in a number of engineering processes such as heat-treated materials travelling between a feed roll and a wind up roll, aerodynamic extrusion of plastic sheets, glass fiber and paper production, cooling of an infinite metallic plate in a cooling path, manufacturing of polymeric sheets are few examples of flow due to stretching surfaces. This work provides a very useful source of information for researchers on this subject.

Such flow analysis is even not available yet for the hydrodynamic fluid. The series solution for MHD boundary layer problem with slip condition by means of MLDM is yet not available in the literature.

The purpose of this paper is to apply an efficient semi-analytical method for the approximate solution of Lienard’s equation of fractional order.

A Laplace decomposition method (LDM) is implemented for the nonlinear fractional Lienard’s equation that is complemented with initial conditions. The nonlinear term is decomposed and then a recursive algorithm is constructed for the determination of the proposed infinite series solution.

A number of examples are tested to explicate the efficiency of the proposed technique. The results confirm that this approach is convergent and highly accurate by using only few iterations of the proposed scheme.

The approach is original and is of value because it is the first time that this approach is used successfully to tackle fractional differential equations, which are of great interest for authors in the recent years.

This paper aims to use the Laplace Adomian decomposition method (LADM) to investigate the effects of thermal convection, thermal conduction, surface emissivity and thermal radiation on the heat dissipated by a continuously moving plate undergoing thermal processing.

In performing the analysis, it is assumed that the thermal conductivity and surface emissivity of the plate are both temperature-dependent. The accuracy of the LADM solutions is confirmed by comparing the results obtained for the temperature distribution within the plate with those reported in the literature based on the differential transformation method.

It is shown that the heat dissipated from the plate reduces as the Peclet number increases. By contrast, the dissipated heat increases as any one of the non-dimensionalized parameters of the system, i.e. Nc, Nr and B, increases. In addition, the temperature drop along the length of the plate reduces as parameter A increases owing to a more rapid heat transfer.

The results provide a useful source of reference for the choice of suitable materials and cooling fluids in a variety of practical applications.

The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are investigated.

In this work, the governing partial differential equations are transformed to a nonlinear ordinary differential equation by using some proper similarity transformations. Then an efficient semi-analytical method, the Laplace Adomian decomposition method (LADM) is applied to obtain semi-analytical solutions of the similarity solutions in both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface. To improve the accuracy and enlarges the convergence domain of the obtained results by the LADM, the study has combined it with Padé approximation.

Accuracy and efficiency of the presented method are illustrated and denoted through the tables and figures. Also the effects of the suction parameter λ and slip parameter K on the fluid velocity and on the tangential stress are investigated.

The similarity solutions of the governing partial differential equation are obtained analytically by using an efficient developed method, namely the Laplace Adomian decomposition-Padé method. The analytic solutions of nonlinear ordinary differential equation are constructed for both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface.

The purpose of this study is to obtain an analytical solution for a nonlinear system of the COVID-19 model for susceptible, exposed, infected, isolated and recovered.

The Laplace decomposition method and the differential transformation method are used.

The obtained analytical results are useful on two fronts: first, they would contribute to a better understanding of the dynamic spread of the COVID-19 disease and help prepare effective measures for prevention and control. Second, researchers would benefit from these results in modifying the model to study the effect of other parameters such as partial closure, awareness and vaccination of isolated groups on controlling the pandemic.

The approach presented is novel in its implementation of the nonlinear system of the COVID-19 model

The purpose of this paper is to propose the Laplace Adomian Decomposition Method (LADM) for studying the nonlinear temperature and thermal stress analysis of annular fins with time-dependent boundary condition.

The nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root is studied by the LADM. The radiation effect is considered. The convective heat transfer coefficient is considered as a temperature function.

The proposed solution method is helpful in overcoming the computational bottleneck commonly encountered in industry and in academia. The results show that the circumferential stress at the root of the fin will be important in the fatigue analysis.

This study presents an effective solution method to analyze the nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root by using LADM.

This study aims to investigate the approximate solution of the time fractional time-fractional Newell–Whitehead–Segel (TFNWS) model that reflects the appearance of the stripe patterns in two-dimensional systems. The significant results of plot distribution show that the proposed approach is highly authentic and reliable for the fractional-order models.

The Laplace transform residual power series method (ℒT-RPSM) is the combination of Laplace transform (ℒT) and residual power series method (RPSM). The ℒT is examined to minimize the order of fractional order, whereas the RPSM handles the series solution in the form of convergence. The graphical results of the fractional models are represented through the fractional order α.

The derived results are obtained in a successive series and yield the results toward the exact solution. These successive series confirm the consistency and accuracy of ℒT-RPSM. This study also compares the exact solutions with the graphical solutions to show the performance and authenticity of the visual solutions. The proposed scheme does not require the restriction of variables and produces the numerical results in terms of a series. This strategy is capable to handle the nonlinear terms very easily for the TFNWS model.

This paper presents the original work. This study reveals that ℒT can perform the solution of fractional-order models without any restriction of variables.

In this article, the author proposed a new analytical solution procedure for 12 order differential equation. The new analytical technique namely homotopy analysis transform method is efficient and effective for solving higher order differential equations. The results indicate the effectiveness and stability of the proposed algorithm. The paper aims to discuss these issues.

The author designed a new solution methodology for higher order differential equations which is a combination of Laplace transformation and homotopy deformation theory.

The author mainly discussed two numerical applications with error analysis of analytical scheme which shows high order accuracy of the projected technique which will serve as a milestone for solving higher order differential equations in engineering with no efforts.

The author proposed an innovative and original idea for nth-order differential equations in this article.