Derivation of a new block method similar to the block trapezoidal rule for the numerical solution of first-order IVPs

Abbas, Salman

doi:10.1080/00207160802172216

Cited by 12 publications

(15 citation statements)

References 11 publications

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“…It should be noted that the method performs better when the step-size is chosen within the stability interval. The Tables 1 and 2 had shown our new method is more efficient in terms of accuracy when compared with the self starting predictor corrector method proposed by [11] and [15]. It should be noted that this method performs better when the step size (h) is within the stability interval.…”

Section: Discussionmentioning

confidence: 99%

A New Block-Predictor Corrector Algorithm for the Solution of y’’’=f(x, y, y’, y’’)

Adesanya¹,

Udo²,

Alkali³

2012

AJCM

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We consider direct solution to third order ordinary differential equations in this paper. Method of collection and interpolation of the power series approximant of single variable is considered to derive a linear multistep method (LMM) with continuous coefficient. Block method was later adopted to generate the independent solution at selected grid points. The properties of the block viz: order, zero stability and stability region are investigated. Our method was tested on third order ordinary differential equation and found to give better result when compared with existing methods.

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Section: Discussionmentioning

confidence: 99%

A New Block-Predictor Corrector Algorithm for the Solution of y’’’=f(x, y, y’, y’’)

Adesanya¹,

Udo²,

Alkali³

2012

AJCM

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“…In Zanariah et al (2012 a two-point four step direct implicit block method of order 7 for solving third order ordinary differential equations using variable step size strategy was proposed. In this paper, the works of Shampine and Watt (1969) and Abbas (2006) were adopted. They gave the general discrete block formula as:…”

Section: Introductionmentioning

confidence: 99%

“…According to Abbas (2006), (1.4) is called block predictor-corrector method and self-starting since the prediction equation is obtained directly from the general block formula (1.2).…”

Section: Introductionmentioning

confidence: 99%

Direct Block Predictor-Corrector Method for the Solution of General Fourth Order Odes

Olabode¹,

Alabi²

2013

JMR

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This article presented the direct block predictor-corrector method for solving general higher order initial value problems of ordinary differential equation. Method of collocation and interpolation of power series approximate solution was used to derive a continuous linear multistep method. Block method was later used to generate the non overlapping solution at selected grid points. The method developed, is self starting, consistent, symmetric, zero-stable and convergent. The performance of the new block method was tested with some fourth order initial value problems and it was found to compare favorably with the existing methods.

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“…This block method has the properties of Runge-kutta method for being self-starting and does not require development of separate predictors or starting values. Among these authors are [7][8][9][10][11][12]. Block method was found to be cost effective and gave better approximation.…”

Section: Introductionmentioning

confidence: 99%

Half-Step Continuous Block Method for the Solutions of Modeled Problems of Ordinary Differential Equations

James¹,

Adesanya²,

Sunday³

et al. 2013

AJCM

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In this paper, we developed a new continuous block method using the approach of collocation of the differential system and interpolation of the power series approximate solution. A constant step length within a half step interval of integration was adopted. We evaluated at grid and off grid points to get a continuous linear multistep method. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent and zero stable hence convergent. The new method was tested on real life problems namely: SIR model, Growth model and Mixture Model. The results were found to compete favorably with the existing methods in terms of accuracy and error bound.

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Derivation of a new block method similar to the block trapezoidal rule for the numerical solution of first-order IVPs

Cited by 12 publications

References 11 publications

A New Block-Predictor Corrector Algorithm for the Solution of y’’’=f(x, y, y’, y’’)

A New Block-Predictor Corrector Algorithm for the Solution of y’’’=f(x, y, y’, y’’)

Direct Block Predictor-Corrector Method for the Solution of General Fourth Order Odes

Half-Step Continuous Block Method for the Solutions of Modeled Problems of Ordinary Differential Equations

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