Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.

Application of the Modified Adomian Decomposition Method on a Mathematical Model of COVID-19

In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (RC) was calculated via the next generation matrix method. We also used the Lyaponuv method to show the global stability of both the disease free and endemic equilibrium points. The results showed that the disease-free equilibrium point is globally asymptotically stable if RC RC > 1. We further used the Adomian decomposition method and the modified Adomian decomposition method to obtain the solutions of the model. Numerical analysis of the model was done using Sagemath 9.0 software.

Solving Different Types of Differential Equations Using Modified and New Modified Adomian Decomposition Methods

The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann conditions is proposed. The scheme is based on the modified Adomian decomposition method and the inverse linear operator theorem. Several differential equations with Neumann boundary conditions are solved to demonstrate the high accuracy and efficiency of the proposed scheme.

On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.

Adomian Decomposition Method for Solving Boussinesq Equations Using Maple

This paper uses the Adomian Decomposition Method (ADM) to solve Boussinesq equations using Maple. The Boussinesq approximation for water waves is a weakly nonlinear and long-wave approximation in fluid dynamics. The approximation is named after Joseph Boussinesq, who developed it in response to John Scott Russell’s observation of a wave of translation (also known as solitary wave or soliton). Bossinesq’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. In this paper, we investigate a nonlinear singly perturbed advection-diffusion problem. Using the usual Adomian Decomposition Method, we formulate an approximate linear advection-diffusion problem and investigate several practical numerical approaches for solving it (ADM). The Adomian Decomposition Method (ADM) is a powerful tool for numerical simulations and approximation analytic solutions. The Adomian Decomposition Method (ADM) is used to solve nonlinear advection differential equations using Maple by illustrating numerous examples. The findings are presented in the form of tables and graphs for several examples. For various examples, the findings are presented in the form of tables and graphs. The difference between the precise and numerical solutions indicates the Maple program solution’s efficacy, as well as the ease and speed with which it was acquired.

The Natural Transform Decomposition Method for Solving Fractional Klein-Gordon Equation

In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.

Adomian Decomposition Method for Solving Time Fractional Burgers Equation Using Maple

In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.

On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.

Numerical Treatment of Initial Value Problems of Nonlinear Ordinary Differential Equations by Duan-Rach-Wazwaz Modified Adomian Decomposition Method

We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Padé approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist.

Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method

In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.

SOLUTION OF SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS BY ADOMIAN DECOMPOSITION METHOD

The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffier functions of matric argument. The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1, the result here is simplified to that of first order differential equation.

ON DECOMPOSITION METHOD FOR ACOUSTIC WAVE SCATTERING BY MULTIPLE OBSTACLES

Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented.

A Fully Nonlinear HOBEM with the Domain Decomposition Method for Simulation of Wave Propagation and Diffraction

A higher-order boundary element method(HOBEM) for simulating the fully nonlinear regular wave propagation and diffraction around a fixed vertical circular cylinder is investigated. The domain decomposition method with continuity conditions enforced on the interfaces between the adjacent sub-domains is implemented for reducing the computational cost. By adjusting the algorithm of iterative procedure on the interfaces, four types of coupling strategies are established, that is, Dirchlet/Dirchlet-Neumman/Neumman(D/D-N/N), Dirchlet-Neumman(D-N),Neumman-Dirchlet(N-D) and Mixed Dirchlet-Neumman/Neumman-Dirchlet(Mixed D-N/N-D). Numerical simulations indicate that the domain decomposition methods can provide accurate results compared with that of the single domain method. According to the comparisons of computational efficiency, the D/D-N/N coupling strategy is recommended for the wave propagation problem. As for the wave-body interaction problem, the Mixed D-N/N-D coupling strategy can obtain the highest computational efficiency.

A decomposition method of nuclear magnetic resonance T2 spectrum for identifying fluid properties

Based on analysis of NMR T2 spectral characteristics,a new method for identifying fluid properties by decomposing T2 spectrum through signal analysis has been proposed.Because T2 spectrum satisfies lognormal distribution on transverse relaxation time axis,the T2 spectrum can be decomposed into 2 to 5 independent component spectra by fitting the T2 spectrum with Gauss functions.By analyzing the free relaxation response characteristics of crude oil and formation water,the dynamic response characteristics of the core mutual drive between oil and water,the petrophysical significance of each component spectrum is clarified.T2 spectrum can be decomposed into clay bound water component spectrum,capillary bound fluid component spectrum,micropores fluid component spectrum and macropores fluid component spectrum.According to the nature of crude oil in the target area,the distribution range of T2 component spectral peaks of oil-bearing reservoir is 165-500 ms on T2 time axis.This range can be used to accurately identify fluid properties.This method has high adaptability in identifying complex oil and water layers in low porosity and permeability reservoirs.

Adomian decomposition method and Padé approximants for solving the Blaszak-Marciniak lattice

The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.

Nonlinear Problems via a Convergence Accelerated Decomposition Method of Adomian

The present paper is devoted to the convergence control and accelerating the traditional Decomposition Methodof Adomian (ADM). By means of perturbing the initial or early terms of the Adomian iterates by adding aparameterized term, containing an embedded parameter, new modified ADM is constructed. The optimal value ofthis parameter is later determined via squared residual minimizing the error. The failure of the classical ADM is alsoprevented by a suitable value of the embedded parameter, particularly beneficial for the Duan–Rach modification ofthe ADM incorporating all the boundaries into the formulation. With the presented squared residual error analysis,there is no need to check out the results against the numerical ones, as usually has to be done in the traditional ADMstudies to convince the readers that the results are indeed converged to the realistic solutions. Physical examplesselected from the recent application of ADM demonstrate the validity, accuracy and power of the presented novelapproach in this paper. Hence, the highly nonlinear equations arising from engineering applications can be safelytreated by the outlined method for which the classical ADM may fail or be slow to converge.

Analytical solution of fractionally damped beam by Adomian decomposition method

The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional derivatives.

On the Application of the Adomian’s Decomposition Method to a Generalized Thermoelastic Infinite Medium with a Spherical Cavity in the Framework Three Different Models

A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot model,also known as“coupled thermoelasticity”model;the Lord-Shulman model,also referred to as“generalized thermoelasticity with one-relaxation time”approach;and the Green-Lindsay model,also called“generalized thermoelasticity with two-relaxation times”approach.The Adomian’s decomposition method is used to solve the related mathematical problem.The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain.Numerical results for the temperature,radial stress,strain,and displacement are represented graphically.It is shown that the angular thermal load and the relaxation times have significant effects on all the studied fields.

The Adomian Decomposition Method for Solving Volterra-Fredholm Integral Equation Using Maple

In this paper, Adomian decomposition method (ADM) is used to solve the Volterra-Fredholm integral equation. A number of examples have been presented to explain the numerical results, which is the comparison between the exact solution and the numerical solution, and it is found through the tables and the amount of error between the exact solution and the numerical solution, it is very small and almost non-existent and is also illustrated through the graph how the exact solution of completely applies to the numerical solution This proves the accuracy of the method, which is the Adomian decomposition method (ADM) for solving the Volterra Fredholm integral equation using Maple 18. And that this method is characterized by ease, speed and great accuracy in obtaining numerical results.