4. Wong, Y-C. 1963. A global formulation of the condition for a curve to Lie in a sphere, Monatshefte für Mathematik, 67(4), 363-365.
5. Reuleaux, F, The Kinematics of Machinery; Trans. By Kennedy A.B.W. Dover Publishers: New York, 1963.
6. Gluck. H. 1966. Higher curvatures of curves in Euclidean space, The American Mathematical Montly, 73, 699-704.
7. Bruer, S, Gottlieb, D. 1971. Explicit characterization of spherical curves, Proceedings of the American Mathematical Society, 27(1), 126-127.
8. Dannon, V. 1981. Integral characterizations and the theory of curves, Proceedings of the American Mathematical Society, 81(4), 600-602.
9. Sezer, M, Integral properties and applications of a Frenet-like differential equation system, II. National Mathematical Symposium, Ege University, İzmir, 1989, 1, pp 435-444.
10. Akdoğan, Z, Mağden, A. 2001. Some characterization of curves of constant breadth in En space, Turkish Journal of Mathematics; 25, 433-444.
11. Sezer, M. 1996. A method for the approximate solution of the second order linear differential equations in terms of Taylor Polynomials, International Journal of Mathematical Education in Science and Technology, 27(6), 821- 834.
12. Hacısalihoğlu, H.H, Differential Geometry; Ankara Univ. Press: Ankara, Turkey, 1993.
14. Karger, A, Novak, J, Space Kinematics and Lie Groups; Gordon And Breach Science Publishers: 1985.
15. Millman, R.S, Parker, G.D, Elements of Differential Geometry; Prentice-Hall, Inc., Englewood Cliffs Press: New Jersey, 1977.
Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space
In this study we consider a third order linear differential equation
with variable coefficients characterizing spherical curves according to Frenet
frame in Euclidean 4-Space . This equation whose coefficients are related to special function,
curvature and torsion, is satisfied by the position vector of any regular unit
velocity spherical curve. These type equations are generally impossible to
solve analytically and so, for approximate solution we present a numerical method
based on Taylor polynomials and collocations points by using initial
conditions. Our method reduces the solution of problem to the solution of a
system of algebraic equations and the approximate solution is obtained in terms
of Taylor polynomials.
4. Wong, Y-C. 1963. A global formulation of the condition for a curve to Lie in a sphere, Monatshefte für Mathematik, 67(4), 363-365.
5. Reuleaux, F, The Kinematics of Machinery; Trans. By Kennedy A.B.W. Dover Publishers: New York, 1963.
6. Gluck. H. 1966. Higher curvatures of curves in Euclidean space, The American Mathematical Montly, 73, 699-704.
7. Bruer, S, Gottlieb, D. 1971. Explicit characterization of spherical curves, Proceedings of the American Mathematical Society, 27(1), 126-127.
8. Dannon, V. 1981. Integral characterizations and the theory of curves, Proceedings of the American Mathematical Society, 81(4), 600-602.
9. Sezer, M, Integral properties and applications of a Frenet-like differential equation system, II. National Mathematical Symposium, Ege University, İzmir, 1989, 1, pp 435-444.
10. Akdoğan, Z, Mağden, A. 2001. Some characterization of curves of constant breadth in En space, Turkish Journal of Mathematics; 25, 433-444.
11. Sezer, M. 1996. A method for the approximate solution of the second order linear differential equations in terms of Taylor Polynomials, International Journal of Mathematical Education in Science and Technology, 27(6), 821- 834.
12. Hacısalihoğlu, H.H, Differential Geometry; Ankara Univ. Press: Ankara, Turkey, 1993.
14. Karger, A, Novak, J, Space Kinematics and Lie Groups; Gordon And Breach Science Publishers: 1985.
15. Millman, R.S, Parker, G.D, Elements of Differential Geometry; Prentice-Hall, Inc., Englewood Cliffs Press: New Jersey, 1977.
Ağırman Aydın, T., & Sezer, M. (2019). Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space. Celal Bayar University Journal of Science, 15(1), 1-7. https://doi.org/10.18466/cbayarfbe.416121
AMA
Ağırman Aydın T, Sezer M. Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space. CBUJOS. Mart 2019;15(1):1-7. doi:10.18466/cbayarfbe.416121
Chicago
Ağırman Aydın, Tuba, ve Mehmet Sezer. “Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space”. Celal Bayar University Journal of Science 15, sy. 1 (Mart 2019): 1-7. https://doi.org/10.18466/cbayarfbe.416121.
EndNote
Ağırman Aydın T, Sezer M (01 Mart 2019) Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space. Celal Bayar University Journal of Science 15 1 1–7.
IEEE
T. Ağırman Aydın ve M. Sezer, “Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space”, CBUJOS, c. 15, sy. 1, ss. 1–7, 2019, doi: 10.18466/cbayarfbe.416121.
ISNAD
Ağırman Aydın, Tuba - Sezer, Mehmet. “Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space”. Celal Bayar University Journal of Science 15/1 (Mart 2019), 1-7. https://doi.org/10.18466/cbayarfbe.416121.
JAMA
Ağırman Aydın T, Sezer M. Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space. CBUJOS. 2019;15:1–7.
MLA
Ağırman Aydın, Tuba ve Mehmet Sezer. “Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space”. Celal Bayar University Journal of Science, c. 15, sy. 1, 2019, ss. 1-7, doi:10.18466/cbayarfbe.416121.
Vancouver
Ağırman Aydın T, Sezer M. Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space. CBUJOS. 2019;15(1):1-7.