Yıl 2021,
, 153 - 158, 28.06.2021
Kübra Erdem Biçer
,
Mehmet Sezer
,
Mustafa Kazaz
Kaynakça
- Dannon, V. 1981. Integral Characterizations and Theory of Curves. Proc. Amer. Math. Soc.; 4: 600–603.
- Sezer, M. 1989. Differential Equations and Integral Characterizations for E4- Spherical Curves. Doga Tr. J. Math.; 13: 125–131.
- Köse, Ö. 1986. On Space Curves of Constant Breadth. Doga Tr. J. Math.; 10: 11–14.
- Sezer, M. 1989. Differential Equations Characterizing Space Curves of Constant Breadth and A Criterion for These Curves. Doga Tr. J. Math.; 13: 70–78.
- Do Carmo, MP. Differential Geometry of Curves and Surfaces. Prentice Hall, Inc. Englewood Cliffs, 1976.
- Paşalı Atmaca, S, Akgüller, Ö, Sezer, M. 2013. Integral Characterization of a System of Differential Equations and Applications. Nonl. Analysis and Differential Equations; 1(2): 57-66.
- Çetin, M, Tunçer, Y, Karacan, MK. 2014. Smarandache Curves According to Bishop Frame in Euclidean 3-Space. Gen. Math. Notes; 20(2): 50-66.
- Erdem, K, Yalçinbaş, S. 2012. Numerical approach of linear delay difference equations with variable coefficients in terms of Bernoulli polynomials. AIP Conf. Proc.; 1493: 338-344.
- Erdem, K, Yalçinbaş, S. 2012. Bernoulli Polynomial Approach to High-Order Linear Differential Difference Equations. AIP Conf. Proc.; 1479: 360-364.
- Erdem, K, Yalçinbaş, S, Sezer, M. 2013. A Bernoulli approach with residual correction for solving mixed linear Fredholm integro-differential-difference equation. Journal of Difference Equations and Applications; 19(10): 1619-1631.
- Erdem, K, Yalçinbaş, S. 2016. A matrix approach to solving hyperbolic partial differential equations using Bernoulli polynomials. Filomat; 30(4): 993–1000.
- Erdem, K, Yalçinbaş, S. 2017. Numerical Solutions for Helmholtz Equations using Bernoulli Polynomials. AIP Conf. Proc.; 1863: 300021-1–300021-4.
- Erdem Biçer, K, Sezer, M. 2017. Bernoulli Matrix-Collocation Method for solving General Functional Integro-Differential Equations with Hybrid Delays. Journal of Inequalities and Special Functions; 8(3): 85-99.
- Apostol, TM. Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976, pp 264-267.
- Ates, BY, Çetin, M, Sezer, M. 2015. Taylor polynomial approach for systems of linear differential equations in normal form and residual error estimation. NTMSCI; 3: 116-128.
- Sahiner, B, Sezer, M. 2018. Determining constant breadth curve mate of a curve on a surface via Taylor collocation method. Determining constant breadth curve mate of a curve on a surface via Taylor collocation method. NTMSCI; 6(3): 103-115.
- Cetin, M. Sabit Genişlikli Eğriler Ve Küresel Eğrilerin Diferensiyel Karakterizasyonları. PhD Thesis, Manisa Celal Bayar University, The Institute of Natural and Applied Sciences, 2015.
Numerical Solutions of System of First Order Normalized Linear Differential Equations by Using Bernoulli Matrix Method
Yıl 2021,
, 153 - 158, 28.06.2021
Kübra Erdem Biçer
,
Mehmet Sezer
,
Mustafa Kazaz
Öz
Systems of first order differential equations have been arisen in science and engineering. Specially, the systems of normalized linear differential equations appear in differential geometry and kinematics problems. Solution of them is quite difficult analytically; therefore, numerical methods have need for the approximate solution. In this study, by means of a matrix method related to the truncated Bernoulli series we find the approximate solutions of the Frenet-Like system with variable coefficients upon the initial conditions. This method transforms the mentioned problem into a system of algebraic equations by using the matrix relations and collocation points; so, the required results along with the solutions are obtained and the usability of the method is discussed.
Kaynakça
- Dannon, V. 1981. Integral Characterizations and Theory of Curves. Proc. Amer. Math. Soc.; 4: 600–603.
- Sezer, M. 1989. Differential Equations and Integral Characterizations for E4- Spherical Curves. Doga Tr. J. Math.; 13: 125–131.
- Köse, Ö. 1986. On Space Curves of Constant Breadth. Doga Tr. J. Math.; 10: 11–14.
- Sezer, M. 1989. Differential Equations Characterizing Space Curves of Constant Breadth and A Criterion for These Curves. Doga Tr. J. Math.; 13: 70–78.
- Do Carmo, MP. Differential Geometry of Curves and Surfaces. Prentice Hall, Inc. Englewood Cliffs, 1976.
- Paşalı Atmaca, S, Akgüller, Ö, Sezer, M. 2013. Integral Characterization of a System of Differential Equations and Applications. Nonl. Analysis and Differential Equations; 1(2): 57-66.
- Çetin, M, Tunçer, Y, Karacan, MK. 2014. Smarandache Curves According to Bishop Frame in Euclidean 3-Space. Gen. Math. Notes; 20(2): 50-66.
- Erdem, K, Yalçinbaş, S. 2012. Numerical approach of linear delay difference equations with variable coefficients in terms of Bernoulli polynomials. AIP Conf. Proc.; 1493: 338-344.
- Erdem, K, Yalçinbaş, S. 2012. Bernoulli Polynomial Approach to High-Order Linear Differential Difference Equations. AIP Conf. Proc.; 1479: 360-364.
- Erdem, K, Yalçinbaş, S, Sezer, M. 2013. A Bernoulli approach with residual correction for solving mixed linear Fredholm integro-differential-difference equation. Journal of Difference Equations and Applications; 19(10): 1619-1631.
- Erdem, K, Yalçinbaş, S. 2016. A matrix approach to solving hyperbolic partial differential equations using Bernoulli polynomials. Filomat; 30(4): 993–1000.
- Erdem, K, Yalçinbaş, S. 2017. Numerical Solutions for Helmholtz Equations using Bernoulli Polynomials. AIP Conf. Proc.; 1863: 300021-1–300021-4.
- Erdem Biçer, K, Sezer, M. 2017. Bernoulli Matrix-Collocation Method for solving General Functional Integro-Differential Equations with Hybrid Delays. Journal of Inequalities and Special Functions; 8(3): 85-99.
- Apostol, TM. Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976, pp 264-267.
- Ates, BY, Çetin, M, Sezer, M. 2015. Taylor polynomial approach for systems of linear differential equations in normal form and residual error estimation. NTMSCI; 3: 116-128.
- Sahiner, B, Sezer, M. 2018. Determining constant breadth curve mate of a curve on a surface via Taylor collocation method. Determining constant breadth curve mate of a curve on a surface via Taylor collocation method. NTMSCI; 6(3): 103-115.
- Cetin, M. Sabit Genişlikli Eğriler Ve Küresel Eğrilerin Diferensiyel Karakterizasyonları. PhD Thesis, Manisa Celal Bayar University, The Institute of Natural and Applied Sciences, 2015.