Solution of multiple point, nonlinear boundary value problems by method of weighted residuals

Haque, Md. Ershadul; Baluch, Mohammed H.; Mohsen, M. F. N.

doi:10.1080/00207168608803505

Cited by 10 publications

(6 citation statements)

References 1 publication

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“…As the first example consider the following linear third-order differential equation with its boundary conditions at three different points given as (Haque et al, 1986):…”

Section: Test Examples 51 Examplementioning

confidence: 99%

“…In this example we consider the four-point fourth-order nonlinear ordinary differential equation (Haque et al, 1986)…”

Section: Examplementioning

confidence: 99%

“…Despite the large number of works which have been published on the theoretical aspects of these kinds of problems, few works are available on the numerical analysis of multi-point boundary value problems. To see some numerical methods for solving multi-point ordinary differential equations we refer the interested reader to Haque et al (1986) and Liu and Wu (2002). Dehghan and Shakeri (2011) solved multi-point boundary value problems and they proposed another semianalytical approach which is based on the homotopy analysis method or the homotopy perturbation method (Shakeri and Dehghan, 2008b) (as a special case of the homotopy analysis method).…”

Section: Introductionmentioning

confidence: 99%

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An efficient method for solving multi-point boundary value problems and applications in physics

Tatari

Dehghan

2011

Journal of Vibration and Control

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In this work, multi-point boundary value problems are considered. These problems have important roles in the modelling of various problems in physics and engineering. Although numerous works have been carried out on the existence and uniqueness to the solution of these problems, the numerical or analytical methods are not established for solving them. In this paper the well-known He's variational iteration method is applied for solving the multi-point boundary value problems. The method is modified and the results are shown using some test problems. These results show the efficiency of the new approach.

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“…As the first example consider the following linear third-order differential equation with its boundary conditions at three different points given as (Haque et al, 1986):…”

Section: Test Examples 51 Examplementioning

confidence: 99%

“…In this example we consider the four-point fourth-order nonlinear ordinary differential equation (Haque et al, 1986)…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An efficient method for solving multi-point boundary value problems and applications in physics

Tatari

Dehghan

2011

Journal of Vibration and Control

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“…As the first example consider the following third-order linear differential equation with its boundary conditions at three different points [21] y − k 2 y + a = 0, (3.1)…”

Section: Examplementioning

confidence: 99%

“…Despite of the large amount of works which are done on the theoretical aspects of these kind of equations, few works are available on the numerical analysis of multipoint BVPs. For some numerical methods for solving multipoint ordinary differential equations, refer to [21,22].…”

Section: Introductionmentioning

confidence: 99%

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

Tatari

Dehghan

2006

Phys. Scr.

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In this paper, a method for solving multipoint boundary value problems is presented. The main idea behind this work is the use of the well-known Adomian decomposition method. In this technique, the solution is found in the form of a rapid convergent series. Using this method, it is possible to obtain the solution of the general form of multipoint boundary value problems. The Adomian decomposition method is not affected by computation round off errors and one is not faced with the necessity of large computer memory and time. To show the efficiency of the developed method, numerical results are presented.

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Exact Methods for ODEs**Some of the methods in this section can be used for partial differential equations as well. These methods are indicated by a star (*).

Zwillinger

1989

Handbook of Differential Equations

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Solution of multiple point, nonlinear boundary value problems by method of weighted residuals

Cited by 10 publications

References 1 publication

An efficient method for solving multi-point boundary value problems and applications in physics

An efficient method for solving multi-point boundary value problems and applications in physics

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

Exact Methods for ODEs**Some of the methods in this section can be used for partial differential equations as well. These methods are indicated by a star (*).

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