Mathematics and Statistics Vol. 7(4), pp. 116 - 123
DOI: 10.13189/ms.2019.070404
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Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs

Reem Allogmany ^1,2,*, Fudziah Ismail ^1,3, Zarina Bibi Ibrahim ^1,3
1 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
² Department of Mathematics, Taibah University, Al-Medina, Saudi Arabia
³ Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

ABSTRACT

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 method. Application of the new method is discussed.

KEYWORDS
Implicit, Block Method, Second Order ODEs, Hermite Interpolation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Reem Allogmany , Fudziah Ismail , Zarina Bibi Ibrahim , "Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs," Mathematics and Statistics, Vol. 7, No. 4, pp. 116 - 123, 2019. DOI: 10.13189/ms.2019.070404.

(b). APA Format:
Reem Allogmany , Fudziah Ismail , Zarina Bibi Ibrahim (2019). Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs. Mathematics and Statistics, 7(4), 116 - 123. DOI: 10.13189/ms.2019.070404.