Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

Al-Hayani, Waleed

doi:10.4236/am.2014.510136

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…(e −10w(κ) − 2 (1 + κ) 10 ); 0 ≤ κ ≤ e 1/2−1 subject to BCs; Table 7 analyze the errors at those derivatives where boundary conditions (BCs) are defined in problem 2 at h = 0.064872. We consider the following equation as given in [29,33] w (10) (κ) + e −κ (w(κ)) 2 = e −3κ + e −κ ; 0 ≤ z ' ≤ 1 subject to BCs; w (0) = w (2) Table 10 analyze the errors at those derivatives where boundary conditions (BCs) are defined in problem 3 at h = 1 10 . κ CBS Solution of w (2) (κ), w (4) (κ) CBS Solution of w (1) (κ), w (3)…”

Section: Problemmentioning

confidence: 99%

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A New Scheme Using Cubic B-Spline to Solve Non-Linear Differential Equations Arising in Visco-Elastic Flows and Hydrodynamic Stability Problems

et al. 2019

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This study deals with the numerical solution of the non-linear differential equations (DEs) arising in the study of hydrodynamics and hydro-magnetic stability problems using a new cubic B-spline scheme (CBS). The main idea is that we have modified the boundary value problems (BVPs) to produce a new system of linear equations. The algorithm developed here is not only for the approximation solutions of the 10th order BVPs but also estimate from 1st derivative to 10th derivative of the exact solution as well. Some examples are illustrated to show the feasibility and competence of the proposed scheme.

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Section: Problemmentioning

confidence: 99%

“…Some of the approximate techniques have been established over the years to the numerical solution for these kinds of BVPs. In [2,3], the authors has solved 10 th and 12 th order BVPs using the Adomian decomposition method (ADM) involving Green's function. The homotopy perturbation approach was utilized in [4] to solve BVPs of 10 th order.…”

Section: Introductionmentioning

confidence: 99%

A New Scheme Using Cubic B-Spline to Solve Non-Linear Differential Equations Arising in Visco-Elastic Flows and Hydrodynamic Stability Problems

et al. 2019

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“…It is well known that the ADM allows us to solve nonlinear BVPs without restrictive assumptions such as linearization, discretization and perturbation. Many researchers [14][15][16][17][18][19][20][21][22][23] have shown interest to study the ADM for different scientific models. According to the ADM, we rewrite the problem (1) in an operator form…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of fourth-order Volterra integro-differential equations by the Green’s function and decomposition method

Singh

Wazwaz

2016

Math Sci

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We propose a reliable technique based on Adomian decomposition method (ADM) for the numerical solution of fourth-order boundary value problems for Volterra integro-differential equations. We use Green's function technique to convert boundary value problem into the integral equation before establishing the recursive scheme for the solution components of a specific solution. The advantage of the proposed technique over the standard ADM or modified ADM is that it provides not only better numerical results but also avoids solving a sequence of transcendental equations for unknown constant. Approximations of the solutions are obtained in the form of series. Convergence and error analysis is also discussed. The accuracy and generality of the proposed scheme are demonstrated by solving some numerical examples.

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An extended 3rd-order B-spline strategy to solve linear BVPs rising in stability analysis of electrically conducting fluid in a magnetic field

Khalid

Rehan

Osman

2022

Int. J. Mod. Phys. C

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In this paper, an extended cubic B Spline scheme (CBS) is utilized to solve linear 10th-order boundary value problems (BVPs). Such types of BVPs occur in stability analysis of electrically conducting fluid in a magnetic field. The key concept is that we switched the BVPs to recreate a system that consists of all linear equations. We will alter our problem into such a form that converts the system of 10th-order BVPs and we are struck on a new system of 2nd-order BVPs. The appropriate outcome given by using CBS is contrasted with the accurate root to each problem. For each and every iteration, absolute error is also premeditated. The rule originated here aside from the estimation of the 10th-order BVPs also evaluates derivative from 1st-order to 10th-order of the accurate root. Couple of examples are demonstrated to evidence the adequacy and aptitude of the proffered strategy.

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Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

Cited by 6 publications

References 16 publications

A New Scheme Using Cubic B-Spline to Solve Non-Linear Differential Equations Arising in Visco-Elastic Flows and Hydrodynamic Stability Problems

A New Scheme Using Cubic B-Spline to Solve Non-Linear Differential Equations Arising in Visco-Elastic Flows and Hydrodynamic Stability Problems

Numerical solutions of fourth-order Volterra integro-differential equations by the Green’s function and decomposition method

An extended 3rd-order B-spline strategy to solve linear BVPs rising in stability analysis of electrically conducting fluid in a magnetic field

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