Error Analysis Using Three and Four Stage Eighth Order Embedded Runge-Kutta Method for Sixth Order Ordinary Differential Equation vvi(u)=f(u,v,v',v'',v''',viv)

Authors

  • Manpreet Kaur Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India
  • Sangeet Kumar SGTB Khalsa College, Sri Anandpur Sahib, Punjab, India
  • Jasdev Bhatti Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India

DOI:

https://doi.org/10.37256/cm.4420232610

Keywords:

ordinary differential equations, embedded Runge-Kutta methods, initial value problem, local and global truncation error, zero stability

Abstract

The present paper aims at providing an insight to embedded Runge-Kutta sixth order (RKSD) ordinary differential equation method for solving the initial value problem of order six of type vvi(u) = f(u, v, v', v'',v''',viv). The concept of order conditions for the three and four stages up to the eighth and ninth orders, respectively, is designed and evaluated; furthermore, the zero-stability of the proposed method is proved. Comparisons are made between these orders with the help of a mathematical example, and global and local truncated error norms are evaluated.

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Published

2023-11-15

Issue

Contemporary Mathematics, Volume 4 Issue 4 (2023), 620-1346

Section

Research Article

How to Cite

1.
Error Analysis Using Three and Four Stage Eighth Order Embedded Runge-Kutta Method for Sixth Order Ordinary Differential Equation vvi(u)=f(u,v,v’,v’’,v’’’,viv). Contemp. Math. [Internet]. 2023 Nov. 15 [cited 2025 Dec. 24];4(4):1076-88. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/2610