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A Generalized Series Solution of đť’Źđť’•đť’‰ Order Ordinary Differential Equations

Year 2023, Volume: 20 Issue: 1, 28 - 34, 01.05.2023

Abstract

Differential equations in general play major role in finding solutions to many problems in real life. These real-life problems are modeled by either ordinary differential equations (with uni-variate independent variable) or partial differential equations (with multi- variate independent variables). The solution method adopted is determined by the nature of the differential equation. In this paper, the solution of an 𝑛𝑡ℎ order Ordinary Differential Equation (ODE) is considered. The power series and the conditions for its convergence or otherwise is examined. Also, the index shift in the summation is applied in the simplification of the resulting algebraic expression and with the introduction of the factorial notation, the number of operations required to solve the problem is minimized. The resulting model therefore simplifies the solution method without the rigour of index shit in the summands and algebraic manipulations of the expression obtained. This makes the model applicable to the solution of ordinary differential equation of any order 𝑛. The generalized model is thereafter applied to an ordinary differential equation of order seven without recourse to index shift. This simplified form gives the solution considered and a simple and generalized solution is obtained.

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References

  • E. O. Adeyefa, and A. A. Ibrahim, “A Sixth-order Self-Starting Algorithms for Second Order Initial Value Problems of ODEs” British Journal of Mathematics & Computer Science, vol. 15, no. 2, pp. 1-8, 2016.
  • K. Stroud, “Engineering Mathematics,” Palgrave, New York, 1991.
  • P. Dawkins, “Differential Equations 2007” http//tutorial.math.lamar.edu./terms.aspx. (accessed 25.02.2020).
  • C. H. Edward, Penny, D. E., “Elementary Differential Equations” Pearson Education Inc., New Jersey
  • W. F. Trench, “Elementary Differential Equations” (Free edition)
  • R. Brownson, “Differential Equations Schaum’s Outline Series,” McGraw-Hill, New York
  • J. R. Chasnov, “Differential Equations, Lecture Notes,” The Hong Kong University of Science and Technology, pp. 67-78, 2019.
  • H. K. Dass, “Advanced Engineering Mathematics,” S. Chand & Company Ltd., New Delhi, 2013
  • M. E. Davis, “Numerical Methods and Modeling for Chemical Engineers” John Wiley and Sons, New York, 1984.
  • E. Kreyszig, “Advanced Engineering Mathematics,” John Wiley and Sons, New York, 2011
Year 2023, Volume: 20 Issue: 1, 28 - 34, 01.05.2023

Abstract

Project Number

-

References

  • E. O. Adeyefa, and A. A. Ibrahim, “A Sixth-order Self-Starting Algorithms for Second Order Initial Value Problems of ODEs” British Journal of Mathematics & Computer Science, vol. 15, no. 2, pp. 1-8, 2016.
  • K. Stroud, “Engineering Mathematics,” Palgrave, New York, 1991.
  • P. Dawkins, “Differential Equations 2007” http//tutorial.math.lamar.edu./terms.aspx. (accessed 25.02.2020).
  • C. H. Edward, Penny, D. E., “Elementary Differential Equations” Pearson Education Inc., New Jersey
  • W. F. Trench, “Elementary Differential Equations” (Free edition)
  • R. Brownson, “Differential Equations Schaum’s Outline Series,” McGraw-Hill, New York
  • J. R. Chasnov, “Differential Equations, Lecture Notes,” The Hong Kong University of Science and Technology, pp. 67-78, 2019.
  • H. K. Dass, “Advanced Engineering Mathematics,” S. Chand & Company Ltd., New Delhi, 2013
  • M. E. Davis, “Numerical Methods and Modeling for Chemical Engineers” John Wiley and Sons, New York, 1984.
  • E. Kreyszig, “Advanced Engineering Mathematics,” John Wiley and Sons, New York, 2011
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Adebisi A. Ibrahim 0000-0002-8797-1365

Emmanuel Adeyefa 0000-0003-0942-6430

Project Number -
Publication Date May 1, 2023
Published in Issue Year 2023 Volume: 20 Issue: 1

Cite

APA Ibrahim, A. A., & Adeyefa, E. (2023). A Generalized Series Solution of đť’Źđť’•đť’‰ Order Ordinary Differential Equations. Cankaya University Journal of Science and Engineering, 20(1), 28-34.
AMA Ibrahim AA, Adeyefa E. A Generalized Series Solution of đť’Źđť’•đť’‰ Order Ordinary Differential Equations. CUJSE. May 2023;20(1):28-34.
Chicago Ibrahim, Adebisi A., and Emmanuel Adeyefa. “A Generalized Series Solution of 𝒏𝒕𝒉 Order Ordinary Differential Equations”. Cankaya University Journal of Science and Engineering 20, no. 1 (May 2023): 28-34.
EndNote Ibrahim AA, Adeyefa E (May 1, 2023) A Generalized Series Solution of 𝒏𝒕𝒉 Order Ordinary Differential Equations. Cankaya University Journal of Science and Engineering 20 1 28–34.
IEEE A. A. Ibrahim and E. Adeyefa, “A Generalized Series Solution of 𝒏𝒕𝒉 Order Ordinary Differential Equations”, CUJSE, vol. 20, no. 1, pp. 28–34, 2023.
ISNAD Ibrahim, Adebisi A. - Adeyefa, Emmanuel. “A Generalized Series Solution of 𝒏𝒕𝒉 Order Ordinary Differential Equations”. Cankaya University Journal of Science and Engineering 20/1 (May 2023), 28-34.
JAMA Ibrahim AA, Adeyefa E. A Generalized Series Solution of 𝒏𝒕𝒉 Order Ordinary Differential Equations. CUJSE. 2023;20:28–34.
MLA Ibrahim, Adebisi A. and Emmanuel Adeyefa. “A Generalized Series Solution of 𝒏𝒕𝒉 Order Ordinary Differential Equations”. Cankaya University Journal of Science and Engineering, vol. 20, no. 1, 2023, pp. 28-34.
Vancouver Ibrahim AA, Adeyefa E. A Generalized Series Solution of đť’Źđť’•đť’‰ Order Ordinary Differential Equations. CUJSE. 2023;20(1):28-34.