@article{article_97320, title={Chebyshev Polynomial Solutions of Certain Second Order Non-Linear Differential Equations}, journal={Gazi University Journal of Science}, volume={24}, pages={739–745}, year={2011}, author={Kesan, Cenk}, keywords={Non-linear differential equations, Chebyshev-matrix method, Approximate solution of non-linear}, abstract={<span style="font-size: 10pt; line-height: 150%; mso-ansi-language: EN-US;" lang="EN-US"> <span style="font-family: Times New Roman;"> <p class="MsoNormal" style="text-align: justify; margin: 0cm 46.2pt 0pt 36pt; mso-layout-grid-align: none; mso-pagination: none;"> <span style="font-size: 8pt; mso-no-proof: yes;" lang="EN-GB">The purpose of this study is to give a Chebyshev polynomial approximation for the solution of second-order non-linear differential equations with variable coefficients. For this purpose, Chebyshev matrix method is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the non-linear differential equations. Hence, the result matrix equation can be solved and the unknown Chebyshev coefficients can be found approximately. Additionally, the mentioned method is illustrated by two examples. </span> </p> <p class="MsoNormal" style="text-align: justify; margin: 0cm 46.2pt 0pt 36pt; mso-layout-grid-align: none; mso-pagination: none;"> <span style="font-size: 8pt; mso-no-proof: yes;" lang="EN-GB">  </span> </p> <p class="MsoNormal" style="text-align: justify; margin: 0cm 0cm 0pt;"> <strong style="mso-bidi-font-weight: normal;"> <span style="font-size: 8pt;" lang="EN-GB"> <span style="mso-tab-count: 1;">                </span>Key Words </span> </strong> <span style="font-size: 8pt;" lang="EN-GB">: </span> <span style="font-size: 8pt; mso-bidi-font-style: italic; mso-ansi-language: EN-US; mso-no-proof: yes;" lang="EN-US">Non-linear differential equations, Chebyshev- </span> </p> <p class="MsoNormal" style="text-align: justify; margin: 0cm 0cm 0pt;"> <span style="font-size: 8pt; mso-bidi-font-style: italic; mso-ansi-language: EN-US; mso-no-proof: yes;" lang="EN-US">               matrix method, Approximate solution of  </span> <span style="font-size: 8pt; mso-bidi-font-style: italic; mso-ansi-language: EN-US; mso-no-proof: yes;" lang="EN-US">              non-linear  </span> <span style="font-size: 8pt; mso-bidi-font-style: italic; mso-ansi-language: EN-US; mso-no-proof: yes;" lang="EN-US"> <span style="mso-spacerun: yes;">  </span> </span> </p> <p class="MsoNormal" style="text-align: justify; margin: 0cm 0cm 0pt;"> <span style="font-size: 8pt; mso-bidi-font-style: italic; mso-ansi-language: EN-US; mso-no-proof: yes;" lang="EN-US"> <span style="mso-spacerun: yes;">               </span>ordinary differential equations. </span> <span style="mso-ansi-language: EN-US;" lang="EN-US"> </span> </p> <p class="MsoNormal" style="margin: 0cm 0cm 0pt; line-height: 150%; text-align: justify;">  </p> </span> </span>}, number={4}, publisher={Gazi University}