ANALYTICAL SHOOTING TECHNIQUE FOR THE SOLUTION OF TWO POINT NONLINEAR BOUNDARY VALUE PROBLEMS

Authors

  • Aderibigbe Adebowale Niyi Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria Author
  • Oderinu Razak Adekola Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria Author
  • Bepo Adeyemi Ademola Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria Author

Keywords:

Secant Method, Newton’s Method, Approximate Analytical Solution, Numerical Solution, Adomian decomposition method, Shooting angle

Abstract

In this paper, an analytical approach was used in the scheme of shooting technique to solve two point boundary value problems. The analytical method used was Adomian decomposition method in place of the usual numerical methods which are prone to discretization errors. Boundary value problems were simplified into initial value problems by the technique of shooting and the method of Adomian decomposition was applied to the initial value problems. The slope of the initial condition ( t 0 ) is calculated as the initial shooting angle which was updated as many times as possible by the secant and Newton's method. The updated slope ( t k ) is repeated in the process of shooting until the result is closed enough to hitting the target. 

         Views | Downloads: 90 / 28

Downloads

Download data is not yet available.

References

Adam, B., Hashim, M.H.A. (2014). Shooting method in solving Boundary Value Problem. International Journal of Recent Research and Applied Studies (IJRRAS). 21 (1), 8-30.

Oderinu, R.A., Aregbesola, Y.A.S.: Shooting Method via Taylor Series for Solving Two Point Boundary Value Problem on an infinite Interval. Gen. Math. Notes. 24(1), 74-83 (2014)

Edun, I.F., Akinlabi, G.O. (2021). Application of the shooting method for the solution of second order boundary value problems. Journal of Physics: Conference Series. 1734. doi:10.1088/1742-6596/1734/1/012020.

Masenge, R.P., Malaki, S.S. (2020). Finite Difference and Shooting Methods for Two-Point Boundary Value Problems: A Comparative Analysis. MUST Journal of Research and Development (MJRD). 1(3), 160-170.

Manyonge, A.W., Opiyo, R., Kweyu, D. (2017). Numerical Solution of Non-Linear Boundary Value Problems of Ordinary Differential Equations Using the Shooting Technique. Journal of Innovative Technology and Education. 4(1), 29-36.

Yousif, M.S., Kashiem, B.E., (2013). Solving Linear Boundary Value Problem Using Shooting Continuous Explicit Runge- Kutta Method, Ibn Al-Haitham Journal for Pure & Applied Science. 26(3), 324-330.

Rahman, M.M., Ara, M.J., Islam, M.N., Ali, M.S. (2015). Numerical Study on the Boundary Value Problem by Using a Shooting Method. Pure and Applied Mathematics Journal. 4(3), 96-100.doi: 10.11648/j.pamj.20150403.16.

Agom, E.U., Badmus, A.M. (2015). Application of Adomian Decomposition Method in Solving Second Order Nonlinear Ordinary Differential Equations. International Journal of Engineering Science Invention. 4(11), 60-65.

Mungkasi, S., Ekaputra, M.W. (2018). Adomian decomposition method for solving initial value problems in vibration models. MATEC Web of Conferences, 159. doi.org/10.1051/matecconf/201815902007

Okeke, A.A., Tumba, P., Gambo, J.J. (2019). The Use of Adomian Decomposition Method in Solving Second Order Autonomous and Non-autonomous Ordinary Differential Equations. International Journal of Mathematics and Statistics Invention. 7(1),2321-4759.

Jimoh, A.K., Oyedeji, A.O. (2020). On Adomian decomposition method for solving nonlinear ordinary differential equations of variable coefficients. Open Journal of Mathematical Science. 4, 476-484. doi:10.30538/oms2020.013.

Fadugba, S.E., Zelibe, S.C., Edogbanya, O.H. (2013). On the Adomian Decomposition Method for the Solution of Second Order Ordinary Differential Equations. International Journal of Mathematics and Statistics Studies, 1(2), 20-29.

Erdogan, U., Ozis, T. (2011). A smart nonstandard finite difference scheme for second order nonlinear boundary value problem. Journal of computational physics. 230, 6464-6474.

Agarwal, R.P., O’Regan, D. (2008). An introduction to ordinary differential equations, Eds. pp. 307. Springer, New York.

Downloads

Published

2023-08-01

How to Cite

ANALYTICAL SHOOTING TECHNIQUE FOR THE SOLUTION OF TWO POINT NONLINEAR BOUNDARY VALUE PROBLEMS. (2023). The Journals of the Nigerian Association of Mathematical Physics, 65, 39 – 46. https://nampjournals.org.ng/index.php/home/article/view/18

Share

Similar Articles

1-10 of 53

You may also start an advanced similarity search for this article.