A 5-step maximal order method for direct solution of second order Ordinary Differential Equations

Sj, Kayode; Awoyemi, D. O.

doi:10.4314/jonamp.v9i1.40057

Cited by 10 publications

(11 citation statements)

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“…However, Awoyemi [5], Akinfenwa and Jator [6]developed methods of higher order ODEs directly. The techniques for solving the problem directly are (i) using interpolation and collocation technique, which is the most common, see [7]- [10], and (ii) using interpolation and integration technique. Several studies have been conducted to implement derivative methods in solving ODEs, see [11]- [16].…”

Section: Introductionmentioning

confidence: 99%

Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs

Allogmany¹,

Ismail²,

İbrahim³

2019

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In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates the first and second derivatives of f(x, y, y ), which are the third and fourth derivatives of the solution. The method is derived using Hermite Interpolating Polynomial as the basic function. A performance comparison of the two-point block method is compared in term of accuracy to several existing methods, which have order almost equal or higher than that of the new method. Numerical results interpret the accuracy and efficacy of the new m ethod. Application of the new method is discussed.

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Section: Introductionmentioning

confidence: 99%

Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs

Allogmany¹,

Ismail²,

İbrahim³

2019

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“…Eminent scholars have contributed significantly in their works in this area of research to solving Problem (1) using different numerical methods (Lambert, 1973;Jacques and Judd, 1987;Adee et al, 2005;Awoyemi, 2005;Kayode and Awoyemi, 2005;Awoyemi and Idowu, 2005;Fatunla, 1988;1994;Kayode, 2008a).…”

Section: Introductionmentioning

confidence: 99%

A Multiderivative Collocation Method for 5th Order Ordinary Differential Equations

Kayode¹,

Awoyemi²

2010

Journal of Mathematics and Statistics

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Problem statement: The conventional methods of solving higher order differential equations have been by reducing them to systems of first order equations. This approach is cumbersome and increases computational time. Approach: To address this problem, a numerical algorithm for direct solution of 5th order initial value problems in ordinary differential equations (odes), using power series as basis function, is proposed in this research. Collocation of the differential system is taken at selected grid points to reduce the number of functions to be evaluated per iteration. A number of predictors and their derivatives having the same order of accuracy with the main method are proposed. Results: The approach yields a multiderivative method of order six. Numerical examples solved show increased efficiency of the method with increased number of iterations, converging to the theoretical solutions. Conclusion/Recommendations: The new mutiderivative method is efficient to solve linear and nonlinear fifth order odes without reduction to system of lower order equations

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“…These setbacks had been addressed by some authors 5-7 . In recent times, attempts have been made to formulate numerical algorithms capable of solving problem 1.1 directly using differing methods of derivation with varying degree of accuracy [8][9][10][11][12] . These attempts are not without their associated limitations, some of which include low stepnumber k, too many function evaluations, and the combination of lower-order predictors with the correctors in the predictorcorrector methods 13, 14 .…”

Section: International Journal Of Mathematics and Mathematical Sciencesmentioning

confidence: 99%

An Efficient Zero‐Stable Numerical Method for Fourth‐Order Differential Equations

Kayode

2008

International Journal of Mathematics and Mathematical Sciences

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Recommended by Michael EvansThe purpose of this paper is to produce an efficient zero-stable numerical method with the same order of accuracy as that of the main starting values predictors for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order p 6. The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order p 6.

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A 5-step maximal order method for direct solution of second order Ordinary Differential Equations

Cited by 10 publications

References 0 publications

Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs

Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs

A Multiderivative Collocation Method for 5th Order Ordinary Differential Equations

An Efficient Zero‐Stable Numerical Method for Fourth‐Order Differential Equations

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