scholarly journals Measuring the Pollutants in a System of Three Interconnecting Lakes by the Semianalytical Method

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Indranil Ghosh ◽  
M. S. H. Chowdhury ◽  
Suazlan Mt Aznam ◽  
M. M. Rashid
Keyword(s):  
Differential Equations ◽  
Three Dimensional ◽  
Adomian Decomposition Method ◽  
Dimensional System ◽  
Physical Problems ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Sinusoidal Input ◽  
Semianalytical Method ◽  
Lagrange’S Multipliers

Pollution has become an intense danger to our environment. The lake pollution model is formulated into the three-dimensional system of differential equations with three instances of input. In the present study, the new iterative method (NIM) was applied to the lake pollution model with three cases called impulse input, step input, and sinusoidal input for a longer time span. The main feature of the NIM is that the procedure is very simple, and it does not need to calculate any special type of polynomial or multipliers such as Adomian polynomials and Lagrange’s multipliers. Comparisons with the Adomian decomposition method (ADM) and the well-known purely numerical fourth-order Runge-Kutta method (RK4) suggest that the NIM is a powerful alternative for differential equations providing more realistic series solutions that converge very rapidly in real physical problems.

scholarly journals Mathematical Modelling in Engineering with Integral Transforms via Modified Adomian Decomposition Method

2021 ◽  
Vol 8 (3) ◽  
pp. 409-417
Author(s):  
Minakshi Mohanty ◽  
Saumya Ranjan Jena ◽  
Satya Kumar Misra
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Integral Transforms ◽  
Physical Problems ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Different Types ◽  
Linear Differential ◽  
Homogeneous Linear

In this work three integral transforms through modified Adomian decomposition method (ADM) are proposed to obtain the approximate analytical solution of different types of mathematical models arising in physical problems. These transformations are applied for both homogeneous and non-homogeneous linear differential equations. The efficiency and accuracy of the proposed methods are implemented through higher order non-homogeneous ordinary differential equations. Numerical tests are reported for applicability of the current scheme based on different transformations and compared with exact solutions.

scholarly journals A Hermite Polynomial Approach for Solving the SIR Model of Epidemics

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 305 ◽  
Author(s):  
Aydin Secer ◽  
Neslihan Ozdemir ◽  
Mustafa Bayram
Keyword(s):  
Collocation Method ◽  
Hermite Polynomials ◽  
Three Dimensional ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Equation System ◽  
Dimensional System ◽  
Nonlinear Odes ◽  
Adomian Decomposition ◽  
The Matrix

In this paper, the problem of the spread of a non-fatal disease in a population is solved by using the Hermite collocation method. Mathematical modeling of the problem corresponds to a three-dimensional system of nonlinear ODEs. The presented scheme reduces the problem to a nonlinear algebraic equation system by expanding the approximate solutions by using Hermite polynomials with unknown coefficients. These coefficients of the Hermite polynomials are computed by using the matrix operations of derivatives together with the collocation method. Maple software is used to carry out the computations. In addition, comparison of our method with the Homotopy perturbation method (HPM) and Laplece-Adomian decomposition method (LADM) proves accuracy of solution.

Numerical Simulation for Flow Through Conducting Metal and Metallic Oxide Nanofluids

2020 ◽  
Vol 9 (4) ◽  
pp. 354-361
Author(s):  
P. K. Pattnaik ◽  
S. R. Mishra ◽  
Ram Prakash Sharma
Keyword(s):  
Metal Oxide Nanoparticles ◽  
Three Dimensional ◽  
Adomian Decomposition Method ◽  
Metallic Oxide ◽  
Electrically Conducting ◽  
Number Comparison ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Analytical Result ◽  
Exponentially Stretching

Present paper aims to analyze three-dimensional (3D) motion of an electrically conducting nanofluid past an exponentially stretching sheet. Both metal and metal oxide nanoparticles (such as Cu, Al2O3, TiO2) in the base fluid (water) are examined. Nonlinear ordinary differential systems are obtained by suitable transformations. The crux of the analysis is the development of an estimated analytical result obtained by employing the “Adomian Decomposition Method” (ADM), an approximate analytical method. Momentum and energy descriptions with prescribed boundary conditions are employed. The velocity components and temperature are analyzed. Tabulated values are organized aimed at the outcomes of skin-friction coefficients and Nusselt number. Comparison with past limiting results is shown. Finally, the outstanding outcomes of the present result are; the velocity profile with the inclusion of particle concentration and magnetic parameter decelerate significantly and Al2O3 nanoparticles are favorable for the enhancement in the rate of heat transfer.

scholarly journals A comparison of Adomian decomposition method and RK4 algorithm on Volterra integro differential equations of 2nd kind

2015 ◽  
Vol 4 (4) ◽  
pp. 481
Author(s):  
Kekana M.C ◽  
Shatalov M.Y ◽  
Moshokoa S.P
Keyword(s):  
Differential Equations ◽  
Infinite Series ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Adomian Decomposition

In this paper, Volterra Integro differential equations are solved using the Adomian decomposition method. The solutions are obtained in form of infinite series and compared to Runge-Kutta4 algorithm. The technique is described and illustrated with examples; numerical results are also presented graphically. The software used in this study is mathematica10.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals The Modified Sadik Decomposition Method to Solve a System of Nonlinear Fractional Volterra Integro-Differential Equations of Convolution type

2021 ◽  
Vol 20 ◽  
pp. 335-343
Author(s):  
Prapart Pue-On
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Explicit Form ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Initial Solution ◽  
Convolution Type ◽  
Adomian Decomposition

In this work, an incorporated form of Sadik transform and Adomian decomposition method which is called the Sadik decomposition method is presented. The method is applied to solve a system of nonlinear fractional Volterra integro-differential equations in the convolution form. To avoid collecting the noise terms that lead the method to fail for seeking the solution, the proposed method is modified by selecting a suitable initial solution. The obtained results are expressed in the explicit form of a power series with easily computable terms. In addition, illustrative examples are shown to demonstrate the effectiveness of the method.

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