NEW FORMULAS FOR ADJUSTING SHOOTING ANGLE IN
APPLICATION OF SHOOTING METHOD TO
BOUNDARY VALUE PROBLEMS
Razaq Adekola Oderinu1, Johnson Adekunle Owolabi2,
Saheed Alao3
1Department of Mathematics
Ladoke Akintola University of Technology
Ogbomoso - PMB 4000, NIGERIA
2Department of Mathematics
Bowen University, Iwo
Osun State - PMB 284, NIGERIA 3Department of Mathematics
Ladoke Akintola University of Technology
Ogbomoso - PMB 4000, NIGERIA

Abstract

Two new formulas for adjusting shooting angle in the technique of shooting method were formulated. These formulas are modified Newton’s formula and a Cubic Newton’s formula which were obtained to form Taylor series. The effectiveness of these formulas were investigated by solving two different nonlinear boundary value problems, the results obtained were compared with the regular Newton’s formula and both the new methods performed better that the Newton’s method with the Cubic having the best performance. This inference is evident from the table of errors, tolerance value which is the absolute difference between two successive iterations also gave credence to the performance of the two formulas.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 6
Year: 2022

DOI: 10.12732/ijam.v35i6.3

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References

  1. [1] K. George and E.H. Twizell. Stable second-order finite-difference methods for linear initial-boundary-value problems, Applied Mathematics Letters, 19, No 2 (2006), 146-154.
  2. [2] G.D. Smith, G.D. Smith, and G.D.S. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, 1985.
  3. [3] P.K. Pandey, A finite difference method for the numerical solving general third order boundary-value problem with an internal boundary condition, Russian Mathematics, 61, No 12 (2017), 29-38.
  4. [4] M. Matinfar and M. Ghasemi, Solving BVPs with shooting method and VIMHP, Journal of the Egyptian Mathematical Society, 21, No 3 (2013), 354-360.
  5. [5] Q.M. Al-Mdallal, M.I. Syam, and M.N. Anwar, A collocation-shooting method for solving fractional boundary value problems, Communications in Nonlinear Science and Numerical Simulation, 15, No 12 (2010), 3814- 3822.
  6. [6] R.A. Oderinu and Y.A.S. Aregbesola, Shooting method via taylor series for solving two point boundary value problem on an infinite interval, Gen. Math. Notes, 24, No 1 (2014), 74-83.
  7. [7] R.A. Oderinu and Y.A.S. Aregbesola, Iterative shooting method for solving two-point boundary value problem on an infinite interval, Pioner J. of Math. and Math. Sci. 5, No 1 (2012), 87-94.
  8. [8] R.A. Oderinu and Y.A.S. Aregbesola, Using Laguerre’s quadrature in the weighted residual method for problems with semi-infinite domain, Int. J. Pure Appl. Math., 75 (2012), 76-82.
  9. [9] R.A. Oderinu and Y.A.S. Aregbesola, Weighted residual method in a semi infinite domain using an un-partition methods, International Journal of Applied Mathematics, 25, No 1 (2012), 25-31.
  10. [10] K.S. Sahu and M.K. Jena, Combining the shooting method with an operational matrix method to solve two point boundary value problems, International Journal of Applied and Computational Mathematics, 7, No 2 (2021), 1-19.
  11. [11] B. Pan, Y. Wang, and S. Tian, A high-precision single shooting method for solving hypersensitive optimal control problems, Mathematical Problems in Engineering (2018).