Note on starting the Numerov method more accurately by a hybrid formula of order four for an initial—value problem

Adee, S. O.; Onumanyi, P.; Sirisena, U. W.; Yahaya, Y. A.

doi:10.1016/j.cam.2004.06.016

Cited by 12 publications

(14 citation statements)

References 1 publication

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“…Direct method of solving higher order ordinary differential equations in predictor-corrector mode have been studied by many scholars including: Awoyemi (2003), Adee et al (2005), Awoyemi and Idowu (2005), Fatunla (1994), Kayode (2009), Awoyemi and Kayode (2005) to mention but a few. Awoyemi (2003) investigated a p-stable linear multistep method for general third order initial value problems of ordinary differential equations.…”

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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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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“…Consider a numerical method for solving general first order initial value problems of ordinary differential equations of the form: 0 ( , ), (0) y f x y y y ′ = = (1) where is a continuous function and satisfies Lipschitz condition of the existence and uniqueness of solution. Many authors have proposed solution for first order initial value problems of ordinary differential equations using different approaches.…”

Section: Introductionmentioning

confidence: 99%

“…Many authors have proposed solution for first order initial value problems of ordinary differential equations using different approaches. This work will adopt the block method technique for solving (1) as suggested by researchers. [4], considered the Continuous implicit hybrid one step methods for the solution of initial value problems of general second order ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…[11], developed a new Butcher type two-step block hybrid multistep method for accurate and efficient parallel solution of ordinary differential equations. [1], used hybrid formula of order four to generate starting values for Numerov method. [3], developed linear multistep hybrid methods with continuous coefficients for solving stiff ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

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On One Justification on the Use of Hybrids for the Solution of First Order Initial Value Problems of Ordinary Differential Equations

Mahwash¹

2017

PAMJ

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This paper is aimed at discussing and comparing the performance of standard method with its hybrid method of the same step number for the solution of first order initial value problems of ordinary differential equations. The continuous formulation for both methods was obtained via interpolation and collocation with the application of the shifted Legendre polynomials as approximate solution which was evaluated at some selected grid points to generate the discrete block methods. The order, consistency, zero stability, convergent and stability regions for both methods were investigated. The methods were then applied in block form as simultaneous numerical integrators over non-overlapping intervals. The results revealed that the hybrid method converges faster than the standard method and has minimum absolute error values.

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“…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%

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.

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Note on starting the Numerov method more accurately by a hybrid formula of order four for an initial—value problem

Cited by 12 publications

References 1 publication

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

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

On One Justification on the Use of Hybrids for the Solution of First Order Initial Value Problems of Ordinary Differential Equations

A New Block Method for Special Third Order Ordinary Differential Equations

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