Numerical Solution of Fourth Order Linear Differential Equations by Adomian Decomposition Method

Agom, E. U.; Ogunfiditimi, F. O.; Tahir, Alhaji

doi:10.9734/bjmcs/2016/24714

Cited by 5 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The concept of ADM has been widely reported in literature this include Adomian himself in [7], [1], [2] and [8]. It is well known that in the vicinity of regular point any ordinary differential equation or system of differential equations may be represented by a normal system of ordinary differential equations of the first order in respect to the unknown function, yi = yi(t), iεZ.…”

Section: Concept Of Admmentioning

confidence: 99%

“…This has also been reported in [1] that the solution of equation (2.1) is Generally, ADM is equivalent to the perturbation of the governing equations and its solution in respect of a grouping parameter λ which is introduced in calculating the Adomian polynomials. For extensive details and its calculations see [1], [8], [11] and [2].…”

Section: Concept Of Admmentioning

confidence: 99%

“…For nonlinear boundary value problems their analytic solution are obtained only in rare cases. Recently, [1] applied the multistage decomposition method to obtain numerical solutions to this class of equations, while the linear case is given in [2]. The existence and uniqueness solution for the linear case can be found everywhere in literature especially in [3].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cubic B-Spline Collocation and Adomian Decomposition Methods on 4th Order Multi-point Boundary Value Problems

Agom

Ogunfiditimi

Eno

et al. 2018

JAMCS

Self Cite

View full text Add to dashboard Cite

In this paper, Cubic B-Spline collocation method (CBSCM) and Adomian Decomposition Method (ADM) are applied to obtain numerical solutions to fourth-order linear and nonlinear differential equations. The CBSCM was based on finite element method involving collocation method with cubic B-spline as a basis function. While ADM was based on multistage decomposition method. We discovered in the illustrative examples considered, that result by ADM were compatible with the closed form solutions well over twenty, in some cases over thirty, decimal places and with extremely minimal absolute errors. Results by CBSCM gave correct solutions to atmost six decimal places with sizeable absolute errors. These has further revealed the importance and superiority of ADM over CBSCM in providing semi-analytic solution to this class of differential equations.

show abstract

Section: Concept Of Admmentioning

confidence: 99%

Section: Concept Of Admmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cubic B-Spline Collocation and Adomian Decomposition Methods on 4th Order Multi-point Boundary Value Problems

Agom

Ogunfiditimi

Eno

et al. 2018

JAMCS

Self Cite

View full text Add to dashboard Cite

show abstract

“…The solution of (14) by the traditional ADM was slow in convergence to the exact solution. So we explore the Modified ADM by Yahaya and Mingzhu [5] and Neelima and Kumar [6] in conjunction with procedures in Agom and Ogunfiditimi [7] and Agom, et al [8]. The linear operator of (1) …”

Section: Numerical Illustrationmentioning

confidence: 99%

On Adomian Polynomials and its Applications to Lane-Emden Type of Equation

Agom

Ogunfiditimi

Assi

2017

International Journal of Mathematical Research

View full text Add to dashboard Cite

Article History KeywordsAdomian polynomials Adomian decomposition method Lane-Emden.In this paper, we generate the Adomian polynomial for major nonlinear terms which are mostly common in differential equations. And we applied it to Lane-Emden type of equations whose nonlinear terms are exponential functions. The result we obtained by modified Adomian decomposition method (ADM) gave a series solution which is the same as the Taylors series of the exact solution.Contribution/ Originality: This study contributes in the existing literature on the use of Adomian decomposition method. It explicitly provide the Adomian polynomials of frequently occurring nonlinear terms in a linear functional. And, for the first time, applied to obtain an exact solution to the Lane-Emden type of equation.

show abstract

“…Recently, Adomian decomposition method (ADM) [5] has been an effective mathematical tool for obtaining approximate and analytical solutions to some of the nonyielding ordinary and partial differential equations [1], [2], [3], [4], [6], [7] and [12]. And the results are closed to being called exact, in fact exact in many situations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Application of Adomian Decomposition Method to One Dimensional Wave Equations

2016

IJSR

View full text Add to dashboard Cite

Adomian decomposition method (ADM) allows us to obtain the exact solution as an infinite series of functions to several classes of equations. It avoids discretization in space and time induced by classical methods of resolution of functional equations. In this paper, we state the general Adomian decomposition method for the wave equation and apply it to problems of one-dimensional wave equations. Four test problems were used to validate the reliability of the method. In all cases, the method gave exact solution in Taylor's series forms, which were the same as the compact analytical exact solution.

show abstract

Numerical Solution of Fourth Order Linear Differential Equations by Adomian Decomposition Method

Cited by 5 publications

References 0 publications

Cubic B-Spline Collocation and Adomian Decomposition Methods on 4th Order Multi-point Boundary Value Problems

Cubic B-Spline Collocation and Adomian Decomposition Methods on 4th Order Multi-point Boundary Value Problems

On Adomian Polynomials and its Applications to Lane-Emden Type of Equation

Numerical Application of Adomian Decomposition Method to One Dimensional Wave Equations

Contact Info

Product

Resources

About