Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 6 Sayı: 2, 50 - 60, 30.09.2021

Öz

Kaynakça

  • \bibitem{r} {\small G. Dahlquist, "A Special Stability problem for Linear Multi-step Methods", BIT Numerical Mathematics, {\textbf{3}} (1963), 27-43.}
  • \bibitem{r0} {\small E. Hairer, and G. Wanner, "Solving Ordinary Differential Equation II: Stiff and Differential-Algebraic Problems", Springer, Berlin, (1966).}
  • \bibitem{r1} {\small J.V. Baxley, "Some singular nonlinear boundary value problems", SIAM Journal of Math. Analysis, (1991), 463-469.}
  • \bibitem{r2} {\small J.V. Baxley, "Numerical solution of singular nonlinear boundary value problems in: D. Bainov, V. Covachev (Eds.)", 3rd Intemat. Coll. on Numerical Analysis, Utrecht, Bulgaria VSP, (1995), 15-24.}
  • \bibitem{rr3} {\small R. Qu and R. P. Agarwal, "A collocation method for solving a class of singular nonlinear two-point boundary value problems", Journal of Computational and Applied Mathematics, (1997), 147-163.}
  • \bibitem{r3} {\small M.M. Chawla, R. Subramanian, "A new spline method for singular two point boundary value problems", J. Inst. Math. Appl., {\bf 24} (1998), 291-310.}
  • \bibitem{r4} {\small M.M. Chawla, R. Subramanian, H. Sathi, "A fourth order method for a singular two point boundary value problem", BIT, {\bf 28} (1998), 88-97.}
  • \bibitem{r5} {\small Y. Liu, "Solutions of two-point boundary value problems for even-order differential equations", Journal of Mathematical Analysis and Applications, {\bf 323} (2006), 721-740.}
  • \bibitem{r6} {\small O. A. Arqub, Z. Abo-Hammour, S. Momani, and N. Shawagfeh, "Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm", Hindawi Abstract and Applied Analysis, {\bf 2012} (2012), 25pages.}
  • \bibitem{r7} {\small G. Mustafa \& T. Ejaz, "A subdivision collocation method for solving two point boundary value problems of order three", Journal of Applied Analysis and Computation, {\bf 7(3)} (2017), 942-956.}
  • \bibitem{r8} {\small P. K. Pandey, "Solution of two point boundary value problems, a numerical approach: parametric difference method", Applied Mathematics and Nonlinear Sciences, {\bf 3(2)} (2018), 649-658.}
  • \bibitem{r9} {\small F. Ghomanjani and S. Shateyi, "Alternative methods for solving nonlinear two-point boundary value problems", Open Phys, {\bf 16} (2018), 371-374.}
  • \bibitem{r10} {\small M. O. Ogunniran, Y. Haruna, \& R. B. Adeniyi, "Efficient $k$-derivative Methods for Lane-Emden Equations and Related Stiff Problems", Nigerian Journal of Mathematics and Applications, {\bf 28(1)} (2019) 1-17.}
  • \bibitem{r11} {\small M. O. Ogunniran, "A Class of Block Multi-Derivative Numerical Integrator for Singular Advection Equations", Journal of the Nigerian Society of Physical Sciences, {\bf 1} (2019), 62-71.}
  • \bibitem{r12} {\small M. O. Ogunniran, O. A. Tayo, Y. Haruna \& A. F. Adebisi, "Linear Stability Analysis of Runge-kutta Methods for Singular Lane-Emden Equations", Journal of the Nigerian Society of Physical Sciences, {\bf 3} (2020), 134-140.}
  • \bibitem{r13} {\small P. W. Eloe AND J. Henderson, "Two-Point Boundary Value Problems for Ordinary Differential Equations, Uniqueness implies Existences", Proceedings of the American Mathematical Society, (2020), 1-11, https://doi.org/10.1090/proc/15115.}
  • \bibitem{r14} {\small Ravi P. Agarwal, and Petio S. Kelevedjiev, "On the Solvability of Fourth-Order Two-Point Boundary Value Problems", Mathematics, {\bf 8(603)} (2020), 1-19.}

Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems

Yıl 2021, Cilt: 6 Sayı: 2, 50 - 60, 30.09.2021

Öz

This paper contains the formulation of an algorithm for solving two-point singular nonlinear boundary value problems of ordinary differential equations. This method is basically a fourth derivative block method obtained from the collocation and interpolation of an assumed derivatives and functional of a basis function. Its implementation was on the evaluation of derivatives of the given smooth first derivative function $u''(t)$ up to the fourth derivative, at some points $t$. It is proved that the algorithm is consistent, zero-stable and convergent. Errors for uniform step lengths are also investigated. Numerical examples are provided to show the efficiency of the algorithm.

Kaynakça

  • \bibitem{r} {\small G. Dahlquist, "A Special Stability problem for Linear Multi-step Methods", BIT Numerical Mathematics, {\textbf{3}} (1963), 27-43.}
  • \bibitem{r0} {\small E. Hairer, and G. Wanner, "Solving Ordinary Differential Equation II: Stiff and Differential-Algebraic Problems", Springer, Berlin, (1966).}
  • \bibitem{r1} {\small J.V. Baxley, "Some singular nonlinear boundary value problems", SIAM Journal of Math. Analysis, (1991), 463-469.}
  • \bibitem{r2} {\small J.V. Baxley, "Numerical solution of singular nonlinear boundary value problems in: D. Bainov, V. Covachev (Eds.)", 3rd Intemat. Coll. on Numerical Analysis, Utrecht, Bulgaria VSP, (1995), 15-24.}
  • \bibitem{rr3} {\small R. Qu and R. P. Agarwal, "A collocation method for solving a class of singular nonlinear two-point boundary value problems", Journal of Computational and Applied Mathematics, (1997), 147-163.}
  • \bibitem{r3} {\small M.M. Chawla, R. Subramanian, "A new spline method for singular two point boundary value problems", J. Inst. Math. Appl., {\bf 24} (1998), 291-310.}
  • \bibitem{r4} {\small M.M. Chawla, R. Subramanian, H. Sathi, "A fourth order method for a singular two point boundary value problem", BIT, {\bf 28} (1998), 88-97.}
  • \bibitem{r5} {\small Y. Liu, "Solutions of two-point boundary value problems for even-order differential equations", Journal of Mathematical Analysis and Applications, {\bf 323} (2006), 721-740.}
  • \bibitem{r6} {\small O. A. Arqub, Z. Abo-Hammour, S. Momani, and N. Shawagfeh, "Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm", Hindawi Abstract and Applied Analysis, {\bf 2012} (2012), 25pages.}
  • \bibitem{r7} {\small G. Mustafa \& T. Ejaz, "A subdivision collocation method for solving two point boundary value problems of order three", Journal of Applied Analysis and Computation, {\bf 7(3)} (2017), 942-956.}
  • \bibitem{r8} {\small P. K. Pandey, "Solution of two point boundary value problems, a numerical approach: parametric difference method", Applied Mathematics and Nonlinear Sciences, {\bf 3(2)} (2018), 649-658.}
  • \bibitem{r9} {\small F. Ghomanjani and S. Shateyi, "Alternative methods for solving nonlinear two-point boundary value problems", Open Phys, {\bf 16} (2018), 371-374.}
  • \bibitem{r10} {\small M. O. Ogunniran, Y. Haruna, \& R. B. Adeniyi, "Efficient $k$-derivative Methods for Lane-Emden Equations and Related Stiff Problems", Nigerian Journal of Mathematics and Applications, {\bf 28(1)} (2019) 1-17.}
  • \bibitem{r11} {\small M. O. Ogunniran, "A Class of Block Multi-Derivative Numerical Integrator for Singular Advection Equations", Journal of the Nigerian Society of Physical Sciences, {\bf 1} (2019), 62-71.}
  • \bibitem{r12} {\small M. O. Ogunniran, O. A. Tayo, Y. Haruna \& A. F. Adebisi, "Linear Stability Analysis of Runge-kutta Methods for Singular Lane-Emden Equations", Journal of the Nigerian Society of Physical Sciences, {\bf 3} (2020), 134-140.}
  • \bibitem{r13} {\small P. W. Eloe AND J. Henderson, "Two-Point Boundary Value Problems for Ordinary Differential Equations, Uniqueness implies Existences", Proceedings of the American Mathematical Society, (2020), 1-11, https://doi.org/10.1090/proc/15115.}
  • \bibitem{r14} {\small Ravi P. Agarwal, and Petio S. Kelevedjiev, "On the Solvability of Fourth-Order Two-Point Boundary Value Problems", Mathematics, {\bf 8(603)} (2020), 1-19.}
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume VI Issue II
Yazarlar

Muideen Ogunniran 0000-0003-4510-1254

Abdulraouv Alabi Bu kişi benim 0000-0002-4070-3961

Qasim Amobi Bu kişi benim 0000-0002-1657-5576

Sabastine Emmanuel Bu kişi benim 0000-0002-9990-3378

Yayımlanma Tarihi 30 Eylül 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 6 Sayı: 2

Kaynak Göster

APA Ogunniran, M., Alabi, A., Amobi, Q., Emmanuel, S. (2021). Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems. Turkish Journal of Science, 6(2), 50-60.
AMA Ogunniran M, Alabi A, Amobi Q, Emmanuel S. Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems. TJOS. Eylül 2021;6(2):50-60.
Chicago Ogunniran, Muideen, Abdulraouv Alabi, Qasim Amobi, ve Sabastine Emmanuel. “Fourth Derivative Block Method for Solving Two-Point Singular Boundary Value Problems and Related Stiff Problems”. Turkish Journal of Science 6, sy. 2 (Eylül 2021): 50-60.
EndNote Ogunniran M, Alabi A, Amobi Q, Emmanuel S (01 Eylül 2021) Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems. Turkish Journal of Science 6 2 50–60.
IEEE M. Ogunniran, A. Alabi, Q. Amobi, ve S. Emmanuel, “Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems”, TJOS, c. 6, sy. 2, ss. 50–60, 2021.
ISNAD Ogunniran, Muideen vd. “Fourth Derivative Block Method for Solving Two-Point Singular Boundary Value Problems and Related Stiff Problems”. Turkish Journal of Science 6/2 (Eylül 2021), 50-60.
JAMA Ogunniran M, Alabi A, Amobi Q, Emmanuel S. Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems. TJOS. 2021;6:50–60.
MLA Ogunniran, Muideen vd. “Fourth Derivative Block Method for Solving Two-Point Singular Boundary Value Problems and Related Stiff Problems”. Turkish Journal of Science, c. 6, sy. 2, 2021, ss. 50-60.
Vancouver Ogunniran M, Alabi A, Amobi Q, Emmanuel S. Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems. TJOS. 2021;6(2):50-6.