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Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space

Tuba Ağırman Aydın [1] , Mehmet Sezer [2]

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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.

Curves in Euclidean Space, Spherical curves, Taylor matrix method, Frenet frame, Linear differential equations; Matrix and collocation method
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Primary Language en Engineering 22-03-2019 Articles Orcid: 0000-0001-8034-0723Author: Tuba Ağırman Aydın (Primary Author)Country: Turkey Orcid: 0000-0002-7744-2574Author: Mehmet Sezer
 Bibtex @research article { cbayarfbe416121, journal = {Celal Bayar University Journal of Science}, issn = {1305-130X}, eissn = {1305-1385}, address = {Celal Bayar University}, year = {2019}, volume = {15}, pages = {1 - 7}, doi = {10.18466/cbayarfbe.416121}, title = {Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space}, key = {cite}, author = {Ağırman Aydın, Tuba and Sezer, Mehmet} } APA 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. DOI: 10.18466/cbayarfbe.416121 MLA Ağırman Aydın, T , Sezer, M . "Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space". Celal Bayar University Journal of Science 15 (2019): 1-7 Chicago Ağırman Aydın, T , Sezer, M . "Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space". Celal Bayar University Journal of Science 15 (2019): 1-7 RIS TY - JOUR T1 - Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space AU - Tuba Ağırman Aydın , Mehmet Sezer Y1 - 2019 PY - 2019 N1 - doi: 10.18466/cbayarfbe.416121 DO - 10.18466/cbayarfbe.416121 T2 - Celal Bayar University Journal of Science JF - Journal JO - JOR SP - 1 EP - 7 VL - 15 IS - 1 SN - 1305-130X-1305-1385 M3 - doi: 10.18466/cbayarfbe.416121 UR - https://doi.org/10.18466/cbayarfbe.416121 Y2 - 2019 ER - EndNote %0 Celal Bayar University Journal of Science Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space %A Tuba Ağırman Aydın , Mehmet Sezer %T Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space %D 2019 %J Celal Bayar University Journal of Science %P 1305-130X-1305-1385 %V 15 %N 1 %R doi: 10.18466/cbayarfbe.416121 %U 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 (March 2019): 1-7. https://doi.org/10.18466/cbayarfbe.416121