A P-Stable Linear Multistep Method For Solving General Third Order Ordinary Differential Equations

Awoyemi, D. O.

doi:10.1080/0020716031000079572

Cited by 79 publications

(105 citation statements)

References 10 publications

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“…y''' = f(x,y),y(a) = y 0 y'(a)η 0 ,y''(a) = η 1 (1) However, only a limited number of analytical methods are available for solving (1) directly without reducing to a first order system of initial value problems. Some authors have proposed solution to higher order initial value problems of ordinary differential equations using different approaches [1][2][3][4][5] .…”

Section: Introductionmentioning

confidence: 99%

“…Some authors have proposed solution to higher order initial value problems of ordinary differential equations using different approaches [1][2][3][4][5] . In particular Awoyemi and Idowu [2] developed a class hybrid collocation method for third order of ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…In particular Awoyemi and Idowu [2] developed a class hybrid collocation method for third order of ordinary differential equations. Awoyemi [1] derived a p-stable linear multistep method for general third order initial value problems of ordinary differential equations which is to be used in form of predictor-corrector forms and like most linear multistep methods, they require starting values from Runge-Kutta methods or any other onestep methods. The predictors are also developed in the same way as correctors.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Block Method for Special Third Order Ordinary Differential Equations

Olabode¹,

Yusuph²

2009

J. of Mathematics and Statistics

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A linear multistep method for the direct solution of initial value problems of ordinary differential equations was presented in this article. Collocation approximation method was adopted in the derivation of the scheme and then the scheme was applied as simultaneous integrator to special third order initial value problem of ordinary differential equations. The new block method possessed the desirable feature of Runge-Kutta method of being self-starting and eliminated the use of predictors. The 3-step block method is P-stable, consistent and more accurate than the existing one. Experimental results confirmed the superiority of the new scheme over the existing method.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A New Block Method for Special Third Order Ordinary Differential Equations

Olabode¹,

Yusuph²

2009

J. of Mathematics and Statistics

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“…Direct solution of higher order ODEs has been found to be more accurate than when they are reduced to their equivalent system of first order ODEs (see [4], [8], [3], [9]). A lot of scholars such as Awoyemi [4][5] and Omar & Suleiman [11][12][13] amongst others have worked on the derivation of direct method for solving higher order ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Derivation of a Six-Step Block Method for Direct Solution of Second Order Ordinary Differential Equations

Kuboye

Omar

2015

MCA

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Abstract-A new six-step block method for solving second order initial value problems of ordinary differential equations is proposed using interpolation and collocation strategies. In developing this method, the power series adopted as an approximate solution is employed as interpolation equation while its second derivative is used as collocation equation. In addition, the stability properties of the developed method are also established. The numerical results reveal that the new method produces better accuracy if compared to existing methods when solving the same problems.

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“…Many attempts have been made to formulate numerical algorithms capable of solving special problem of type (1) without reducing it to system of first order equations [7], [9], [11], [12] . Multiderivative methods for direct solution of problem (1), taking m = 4, have been considered using canonical polynomial as the basis functions [4], [5] . They produced methods with many function evaluations.…”

Section: Introductionmentioning

confidence: 99%

An Order Six Zero-Stable Method for Direct Solution of Fourth Order Ordinary Differential Equations

Jacob¹

2008

American J. of Applied Sciences

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A zero-stable numerical method for direct solution of fourth order differential equations reduces the computational burden and computer time wastage involved in the method of reducing such equations to a system of first order equations. The method adopted is the collocation of the differential system and the interpolation of the approximate solution to the problem using the power series as a basis function. The method is consistent and symmetric with optimal order p = 6. A consistent and symmetric main predictor of order five is also developed for the evaluation of the implicit scheme.

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A P-Stable Linear Multistep Method For Solving General Third Order Ordinary Differential Equations

Cited by 79 publications

References 10 publications

A New Block Method for Special Third Order Ordinary Differential Equations

A New Block Method for Special Third Order Ordinary Differential Equations

Derivation of a Six-Step Block Method for Direct Solution of Second Order Ordinary Differential Equations

An Order Six Zero-Stable Method for Direct Solution of Fourth Order Ordinary Differential Equations

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