The use of the Adomian decomposition method for solving multipoint boundary value problems

Tatari, Mehdi; Dehghan, Mehdi

doi:10.1088/0031-8949/73/6/023

Cited by 77 publications

(44 citation statements)

References 30 publications

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“…From (24) and the first condition in (50), we have that the solution of this BVP can be written in the form…”

Section: The Fractional Order Differential Equationmentioning

confidence: 99%

“…These techniques were developed by many authors as follows. Tatari and Dehghan [24] gave the solution of the general form of multipoint BVPs using the ADM. Al-Hayani [25] used the ADM with Green's function to solve sixth-order BVPs. Duan and Rach [26] proposed the Duan-Rach modified decomposition method for solving BVPs for higher order nonlinear differential equations.…”

Section: Introductionmentioning

confidence: 99%

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New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems

Sirisubtawee

Kaewta

2017

International Journal of Mathematics and Mathematical Sciences

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We apply new modified recursion schemes obtained by the Adomian decomposition method (ADM) to analytically solve specific types of two-point boundary value problems for nonlinear fractional order ordinary and partial differential equations. The new modified recursion schemes, which sometimes utilize the technique of Duan's convergence parameter, are derived using the DuanRach modified ADM. The Duan-Rach modified ADM employs all of the given boundary conditions to compute the remaining unknown constants of integration, which are then embedded in the integral solution form before constructing recursion schemes for the solution components. New modified recursion schemes obtained by the method are generated in order to analytically solve nonlinear fractional order boundary value problems with a variety of two-point boundary conditions such as Robin and separated boundary conditions. Some numerical examples of such problems are demonstrated graphically. In addition, the maximal errors (ME ) or the error remainder functions (ER ( )) of each problem are calculated.

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“…From (24) and the first condition in (50), we have that the solution of this BVP can be written in the form…”

Section: The Fractional Order Differential Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems

Sirisubtawee

Kaewta

2017

International Journal of Mathematics and Mathematical Sciences

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“…Then, by considering [1][2][3][4][5], the cubic non-polynomial spline scheme was implemented to discretize both equations (3) and (5) to generate two systems of linear equations. There are many other numerical methods which have sought wide interest among researchers and some of them are collocation method [6], adomian decomposition method [7], finite element and finite volume methods [8], finite-difference method [8], non-linear shooting method [9] and precise time integration method [10]. Nonetheless, BVPs were usually solved with three standard approaches which are shooting, finite differences and projections [11].…”

Section: Introductionmentioning

confidence: 99%

Solution of fourth-order two-point BVPs with cubic non-polynomial spline and SOR iterative method

Justine

Sulaiman

2018

J. Fundam and Appl Sci.

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Two-point boundary value problems (BVPs) have numerous applications especially in the modeling of most physical phenomena. In this study, the fourth order two solved by using Successive Over cubic non-polynomial spline scheme a numerical experiment was conducted method and the spline scheme in terms of iterations number, execution time and maximum absolute error at different mesh sizes idea, another iterative method was also conducted which is Gauss numerical analysis, the two-point BVPs scheme were found to be best solved by point boundary value problems (BVPs) have numerous applications especially in the modeling of most physical phenomena. In this study, the fourth order two-point BVPs were using Successive Over-Relaxation (SOR) iterative method after discretized with lynomial spline scheme to generate its corresponding sparse linear system. Then, was conducted to determine the performances of the SOR itera the spline scheme in terms of iterations number, execution time and maximum absolute error at different mesh sizes. In order to assess the performances of this proposed idea, another iterative method was also conducted which is Gauss-Seidel (GS).point BVPs together with the cubic non-polynomial spline solved by using the SOR iterative method.

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“…However, most of the methods developed so far in mathematics are valid only for solving linear differential equations. The decomposition method as developed by the mathematician George Adomian (1922Adomian ( -1996 has been very useful in applied mathematics, the applied sciences and engineering [32,33]. The Adomian decomposition method (ADM) has the advantage that its sequence of approximate solutions converges to the exact solution in the vast majority of important cases for very few prerequisites which are naturally satisfied when modeling physical phenomena, and applications can be easily handled for a wide class of ordinary and partial differential equations encompassing both linear and nonlinear cases [18].…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Option Pricing Model Through the Adomian Decomposition Method

González-Gaxiola

Chávez

Santiago

2015

Int. J. Appl. Comput. Math

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Recently the liquidity of financial markets and transaction costs have become a topic of great interest in financial risk management. In this paper, a hypotetical nonlinear model of option pricing that occurs when the effects of market illiquidity and transaction costs are taken into account and an approximate solution is obtained through the Adomian decomposition method. Finally, two numerical examples are investigated to demonstrate the efficiency of our approach.

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The use of the Adomian decomposition method for solving multipoint boundary value problems

Cited by 77 publications

References 30 publications

New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems

New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems

Solution of fourth-order two-point BVPs with cubic non-polynomial spline and SOR iterative method

A Nonlinear Option Pricing Model Through the Adomian Decomposition Method

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