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The Implementation of Block Algorithm for the Solution of Third Order Oscillatory Problems

Year 2025, Volume: 46 Issue: 3, 563 - 571, 30.09.2025

Kareem Bello , Ajimoti Adam Ishaq , Taiye Oyedepo , Adam Ajimoti Ishaq

https://doi.org/10.17776/csj.1485917

Abstract

The implementation of block algorithm for the direct solution of third order oscillatory problems of the form has been studied in this paper. The methodology is carried out using the procedure of interpolation and collocation. The analysis of the paper was analyzed. Also, on the applications, the results obtained shows that is highly efficient and can handle different equations for which the algorithm was designed for. This is because the computed solution matches the exact solution. In fact, the method obviously performed better than the ones with which we compared our results with. This shows that, the algorithm generates results very fast. Thus, there is economy of time in the computation.

Keywords

Block Algorithm Third order Oscillatory Differential Equation Highly Efficient

Project Number

1

Thanks

Thanks

References

  • [1] Sunday J., On the oscillation criteria and computation of third order oscillatory differential equations. Communication in Mathematics and Applications. 6(4)(2018), 615-625.
  • [2] Stetter, H. A., Development of Ideas, Techniques and implementation. Proceeding of Symposium in Applied Mathematics, 48(1994), 205-224.
  • [3] Sabo, J. Ayinde, A. M., Ishaq, A. A., Ajileye, G., The simulation of one-step algorithms for treating higher order initial value problems, Asian Research Journal of Mathematics. 17(9)(2021), 1-7.
  • [4] Sabo, J., Kyagya, T. Y., Ayinde, A. M., Otaide, I. J., Mathematical simulation of the linear block algorithm for modeling third-order initial value problems. BRICS Journal of Educational Research, 12 (3)(2022), 88-96.
  • [5] Ayinde, A. M., Ibrahim, S., Sabo, J. & Silas, D., The physical application of motion using single step block method, Journal of Material Science Research and Review, 6(4)(2023), 708719.
  • [6] Fasasi, K. M., New continue hybrid constant block method for the solution of third order initial value problem of ordinary differential equations, Academic Journal of Applied Mathematical Sciences. 4(6)(2018), 53-60.
  • [7] Genesio, R. and Tesi, A. Harmonic balance methods for the Analysis of chaotic dynamics in nonlinear systems, Antomatica, 28(3)(1992), 531-548.
  • [8] Lee, K. Y., Fudziah, I., Norazak, S., An accurate block Hybrid collocation method for third order ordinary differential equations. Journal of Applied Mathematics, (2014), 1-9. DOI:10.1155/2014/549597.
  • [9] Hanan, M., Oscillation criteria for third order linear differential equations. Pacific Journal of Mathematics, 11(3)(1961), 919-944.
  • [10] Keller, S. H., In the wake of chaos: Unpredictable order in dynamical systems. University of Chicago Press, (1963) pp. 56.
  • [11] Lorenz, E. N., Deterministic non-periodic flow, Journal of Atmospheric Sciences, 20(2)(1963), 130-141.
  • [12] Puu, T. Attractors, bifurcations and chaos: Nonlinear phenomena in economic. Spring- Verlag: Berlin Heidel-Berge, Germany, (200)
  • [13] Lee, K. Y., Fudziah, I., Norazak, S., An accurate block Hybrid collocation method for third order ordinary differential equations. Journal of Applied Mathematics, (2014), 1-9. DOI:10.1155/2014/549597.
  • [14] Fatunla, S. O., Numerical Methods for Initial Value Problems in Ordinary Differential Equations. Academic Press Inc., New York, (1988) [15] Lambert, J. D. (1973). Computational methods in ordinary differential equations. John Wiley, New York, (1973). [16] Areo, E. A., Omojola, M. T., One-twelveth step continuous block method for the solution of y′′′ = f(x, y, y′, y′′), International Journal of Pure and Applied Mathematics, 114(2)(2017), 165-178. [17] Dahlquist, G. G., Convergence and stability in the numerical integration of ordinary differential equations, Mathematica Scandinavica. 4,(1956), 33-50. [18] Skwame, Y., Dalatu, P.I., Sabo, J. and Mathew, M., Numerical application of third derivative hybrid block methods on third order initial value problem of ordinary differential equations. International Journal of Statistics and Applied Mathematics. 4(6)(2019a), 90-100. [19] Fasasi, K. M., New continue hybrid constant block method for the solution of third order initial value problem of ordinary differential equations, Academic Journal of Applied Mathematical Sciences. 4(6)(2018), 53-60. [20] Adeyeye, O., Omar, Z., New self-starting approach for solving special third order initial value problems, Int. J. Pure Appl. Math. 118(3)(2018), 511-517.

Year 2025, Volume: 46 Issue: 3, 563 - 571, 30.09.2025

Kareem Bello , Ajimoti Adam Ishaq , Taiye Oyedepo , Adam Ajimoti Ishaq

https://doi.org/10.17776/csj.1485917

Abstract

Project Number

1

References

  • [1] Sunday J., On the oscillation criteria and computation of third order oscillatory differential equations. Communication in Mathematics and Applications. 6(4)(2018), 615-625.
  • [2] Stetter, H. A., Development of Ideas, Techniques and implementation. Proceeding of Symposium in Applied Mathematics, 48(1994), 205-224.
  • [3] Sabo, J. Ayinde, A. M., Ishaq, A. A., Ajileye, G., The simulation of one-step algorithms for treating higher order initial value problems, Asian Research Journal of Mathematics. 17(9)(2021), 1-7.
  • [4] Sabo, J., Kyagya, T. Y., Ayinde, A. M., Otaide, I. J., Mathematical simulation of the linear block algorithm for modeling third-order initial value problems. BRICS Journal of Educational Research, 12 (3)(2022), 88-96.
  • [5] Ayinde, A. M., Ibrahim, S., Sabo, J. & Silas, D., The physical application of motion using single step block method, Journal of Material Science Research and Review, 6(4)(2023), 708719.
  • [6] Fasasi, K. M., New continue hybrid constant block method for the solution of third order initial value problem of ordinary differential equations, Academic Journal of Applied Mathematical Sciences. 4(6)(2018), 53-60.
  • [7] Genesio, R. and Tesi, A. Harmonic balance methods for the Analysis of chaotic dynamics in nonlinear systems, Antomatica, 28(3)(1992), 531-548.
  • [8] Lee, K. Y., Fudziah, I., Norazak, S., An accurate block Hybrid collocation method for third order ordinary differential equations. Journal of Applied Mathematics, (2014), 1-9. DOI:10.1155/2014/549597.
  • [9] Hanan, M., Oscillation criteria for third order linear differential equations. Pacific Journal of Mathematics, 11(3)(1961), 919-944.
  • [10] Keller, S. H., In the wake of chaos: Unpredictable order in dynamical systems. University of Chicago Press, (1963) pp. 56.
  • [11] Lorenz, E. N., Deterministic non-periodic flow, Journal of Atmospheric Sciences, 20(2)(1963), 130-141.
  • [12] Puu, T. Attractors, bifurcations and chaos: Nonlinear phenomena in economic. Spring- Verlag: Berlin Heidel-Berge, Germany, (200)
  • [13] Lee, K. Y., Fudziah, I., Norazak, S., An accurate block Hybrid collocation method for third order ordinary differential equations. Journal of Applied Mathematics, (2014), 1-9. DOI:10.1155/2014/549597.
  • [14] Fatunla, S. O., Numerical Methods for Initial Value Problems in Ordinary Differential Equations. Academic Press Inc., New York, (1988) [15] Lambert, J. D. (1973). Computational methods in ordinary differential equations. John Wiley, New York, (1973). [16] Areo, E. A., Omojola, M. T., One-twelveth step continuous block method for the solution of y′′′ = f(x, y, y′, y′′), International Journal of Pure and Applied Mathematics, 114(2)(2017), 165-178. [17] Dahlquist, G. G., Convergence and stability in the numerical integration of ordinary differential equations, Mathematica Scandinavica. 4,(1956), 33-50. [18] Skwame, Y., Dalatu, P.I., Sabo, J. and Mathew, M., Numerical application of third derivative hybrid block methods on third order initial value problem of ordinary differential equations. International Journal of Statistics and Applied Mathematics. 4(6)(2019a), 90-100. [19] Fasasi, K. M., New continue hybrid constant block method for the solution of third order initial value problem of ordinary differential equations, Academic Journal of Applied Mathematical Sciences. 4(6)(2018), 53-60. [20] Adeyeye, O., Omar, Z., New self-starting approach for solving special third order initial value problems, Int. J. Pure Appl. Math. 118(3)(2018), 511-517.
There are 14 citations in total.

Details

Primary Language English
Subjects Numerical Analysis
Journal Section Natural Sciences
Authors

Kareem Bello 0009-0007-6270-7705

Ajimoti Adam Ishaq 0000-0002-2563-0952

Taiye Oyedepo 0000-0001-9063-8806

Adam Ajimoti Ishaq 0000-0002-8931-5708

Project Number 1
Publication Date September 30, 2025
Submission Date May 20, 2024
Acceptance Date March 27, 2025
Published in Issue Year 2025 Volume: 46 Issue: 3

Cite

APA Bello, K., Ishaq, A. A., Oyedepo, T., Ishaq, A. A. (2025). The Implementation of Block Algorithm for the Solution of Third Order Oscillatory Problems. Cumhuriyet Science Journal, 46(3), 563-571. https://doi.org/10.17776/csj.1485917
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