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Generalized Half-Step Hybrid Block for Solving Second Order Ordinary Differential Equations Directly

  • Kamarun Hizam MansorEmail author
  • Zurni Omar
  • Azizah Rohni
Conference paper

Abstract

This paper proposes a new generalized half-step hybrid block method with one off-step point to find the direct solution of second order ordinary differential equations. In developing this method, a power series adopted as an approximate solution is interpolated at \( x_{n} \) and \( x_{n + p} \) points while its second derivatives collocated at all points in the interval i.e. \( x_{n} \), \( x_{n + p} \) and \( x_{{n + \frac{1}{2}}} \) to obtain the main continuous scheme, where \( 0 < p < \frac{1}{2} \). The analysis of the method such as order, zero stability, consistency and convergence is also discussed. The derived method is then compared with the existing methods in terms of accuracy. The numerical results suggest that the new method can be served as a viable alternative to solve the initial value problems of second order.

Keywords

Half-step hybrid block method Second order ordinary differential equations One off-step point Direct solution 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Kamarun Hizam Mansor
    • 1
    Email author
  • Zurni Omar
    • 1
  • Azizah Rohni
    • 1
  1. 1.School of Quantitative Sciences, Universiti Utara MalaysiaSintokMalaysia

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