scholarly journals SPLINES SOLUTIONS OF HIGHER-ORDER BVPs THAT ARISE IN CONSISTENT MAGNETIZED FORCE FIELD

Fractals ◽  
2021 ◽  
Author(s):  
AASMA KHALID ◽  
AKMAL REHAN ◽  
KOTTAKKARAN SOOPPY NISAR ◽  
ABDEL-HALEEM ABDEL-ATY ◽  
MOHAMMED ZAKARYA
Keyword(s):  
Force Field ◽  
Gravitational Force ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Nonlinear Boundary Value Problems ◽  
Transform Method ◽  
B Spline ◽  
Adomian Decomposition ◽  
Differential Transform ◽  
Cubic Polynomial

In this paper, cubic polynomial and nonpolynomial splines are developed to solve solutions of 10th- and 12th-order nonlinear boundary value problems (BVPs). Such types of BVPs occur when a consistent magnetized force field is applied crosswise the fluid in the substance of gravitational force. We will amend our problem into such a form that converts the system of [Formula: see text]th- [Formula: see text] [Formula: see text]th-order BVPs into a new system of [Formula: see text]nd-order BVPs. The appropriate outcomes by using CP Spline and CNP Spline are compared with the exact root. To show the efficiency of our results, absolute errors calculated by using CP Spline and CNP Spline have been compared with other methods like differential transform method, Adomian decomposition method, variational iteration method, cubic B-spline, homotopy perturbation method, [Formula: see text]th- and [Formula: see text]th-order B-spline and our results are very encouraging. Graphs and tables are also presented in the numerical section of this paper.

Oxygen diffusion in a spherical cell subject to nonlinear Michaelis–Menten kinetics: Mathematical analysis by two exact methods

2017 ◽  
Vol 10 (02) ◽  
pp. 1750025
Author(s):  
Hooman Fatoorehchi ◽  
Hossein Abolghasemi ◽  
Laura Villafuerte ◽  
Reza Zarghami
Keyword(s):  
Oxygen Diffusion ◽  
Adomian Decomposition Method ◽  
Spherical Cell ◽  
Time Analysis ◽  
Exact Methods ◽  
Perfect Agreement ◽  
Transform Method ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Differential Transform

A nonlinear model representing oxygen diffusion accompanied by the Michaelis–Menten consumption kinetics inside a spherical cell is solved analytically by the differential transform method (DTM) and the modified Adomian decomposition method (MADM). A perfect agreement between the literature data and the results from the proposed solutions is found. The advantages and drawbacks of the two approaches are discussed and their efficiencies are compared through a CPU-time analysis.

scholarly journals New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mohamed Z. Mohamed ◽  
Tarig M. Elzaki ◽  
Mohamed S. Algolam ◽  
Eltaib M. Abd Elmohmoud ◽  
Amjad E. Hamza
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Modified Method ◽  
Adomian Decomposition ◽  
Fractional Differential

The objective of this paper is to compute the new modified method of variational iteration and the Laplace Adomian decomposition method for the solution of nonlinear fractional partial differential equations. We execute a comparatively newfangled analytical mechanism that is denoted by the modified Laplace variational iteration method (MLVIM) and Laplace Adomian decomposition method (LADM). The effect of the numerical results indicates that the double approximation is handy to execute and reliable when applied. It is shown that numerical solutions are gained in the form of approximately series which are facilely computable.

scholarly journals Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 791 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
Dian Chen Lu ◽  
Marjan Goodarzi
Keyword(s):  
Iteration Method ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Integral Transform ◽  
Integral Transformation ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Integral Transform Method

This study is about the lubrication of a long porous slider in which the fluid is injected into the porous bottom. The similarity transformation reduces the Navier-Stokes equations to couple nonlinear, ordinary differential equations, which are solved by a new algorithm. The proposed technique is based on integral transformation. Apparently, there is great symmetry between proposed method and variation iteration method, Adomian decomposition method but in integral transform method all the boundary conditions are applied, then a recursive scheme is used for the analytical solutions, which is unlike the Variational Iteration Method, Adomian Decomposition Method, and other existing analytical methods. Solutions are obtained for much larger Reynolds numbers, and they are compared with analytical and numerical methods. Effects of Reynolds number on velocity components are presented.

scholarly journals Numerical Approximation of Modified Non-linear SIR Model of Computer Viruses

2019 ◽  
Vol 1 (1) ◽  
pp. 34-48
Author(s):  
Samad Noeiaghdam
Keyword(s):  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Phase Portraits ◽  
Transform Method ◽  
Computer Viruses ◽  
Adomian Decomposition ◽  
Differential Transform ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Residual Errors

In this paper, the non-linear modified epidemiological model of computer viruses is illustrated. For this aim, two semi-analytical methods, the differential transform method (DTM) and the Laplace-Adomian decomposition method (LADM) are applied. The numerical results are estimated for different values of iterations and compared to the results of the LADM and the homotopy analysis transform method (HATM). Also, graphs of residual errors and phase portraits of approximate solutions for n = 5, 10, 15 are demonstrated. The numerical approximations show the performance of the LADM in comparison to the DTM and the HATM.

Semi-analytical treatments of conjugate heat transfer

2012 ◽  
Vol 227 (3) ◽  
pp. 492-503 ◽  
Author(s):  
Mohammad Reza Hajmohammadi ◽  
Seyed Salman Nourazar ◽  
Ali Habibi Manesh
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Temperature Distribution ◽  
Decomposition Method ◽  
Conjugate Heat Transfer ◽  
Adomian Decomposition Method ◽  
Differential Transform Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Differential Transform

A new algorithm is proposed based on semi-analytical methods to solve the conjugate heat transfer problems. In this respect, a problem of conjugate forced-convective flow over a heat-conducting plate is modeled and the integro-differential equation occurring in the problem is solved by two lately-proposed approaches, Adomian decomposition method and differential transform method. The solution of the governing integro-differential equation for temperature distribution of the plate is handled more easily and accurately by implementing Adomian decomposition method/differential transform method rather than other traditional methods such as perturbation method. A numerical approach is also performed via finite volume method to examine the validity of the results for temperature distribution of the plate obtained by Adomian decomposition method/differential transform method. It is shown that the expressions for the temperature distribution in the plate obtained from the two methods, Adomian decomposition method and differential transform method, are the same and show closer agreement to the results calculated from numerical work in comparison with the expression obtained by perturbation method existed in the literature.

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