Year 2019, Volume , Issue , Pages 443 - 451 2019-06-01

A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation
A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation

Berat Karaagac [1] , Yusuf Ucar [2] , N. Murat Yagmurlu [3] , Alaattin Esen [4]

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In the present manuscript, a new numerical scheme is presented for solving the time fractional nonlinear Klein-Gordon equation. The approximate solutions of the fractional equation are based on cubic B-spline collocation finite element method and L2 algorithm. The fractional derivative in the given equation is handled in terms of Caputo sense. Using the methods, fractional differential equation is converted into algebraic equation system that are appropriate for computer coding. Then, two model problems are considered and their error norms are calculated to demonstrate the reliability and efficiency of the proposed method. The newly calculated error norms show that numerical results are in a good agreement with the exact solutions.

In the present manuscript, a new numerical scheme is presented for solving the time fractional nonlinear Klein-Gordon equation. The approximate solutions of the fractional equation are based on cubic B-spline collocation finite element method and L2 algorithm. The fractional derivative in the given equation is handled in terms of Caputo sense. Using the methods, fractional differential equation is converted into algebraic equation system that are appropriate for computer coding. Then, two model problems are considered and their error norms are calculated to demonstrate the reliability and efficiency of the proposed method. The newly calculated error norms show that numerical results are in a good agreement with the exact solutions.

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Primary Language en
Subjects Engineering
Journal Section Research Article
Authors

Author: Berat Karaagac (Primary Author)

Author: Yusuf Ucar

Author: N. Murat Yagmurlu

Author: Alaattin Esen

Bibtex @research article { politeknik428986, journal = {Politeknik Dergisi}, issn = {}, eissn = {2147-9429}, address = {Gazi University}, year = {2019}, volume = {}, pages = {443 - 451}, doi = {10.2339/politeknik.428986}, title = {A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation}, key = {cite}, author = {Karaagac, Berat and Ucar, Yusuf and Yagmurlu, N. Murat and Esen, Alaattin} }
APA Karaagac, B , Ucar, Y , Yagmurlu, N , Esen, A . (2019). A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation. Politeknik Dergisi, (), 443-451. DOI: 10.2339/politeknik.428986
MLA Karaagac, B , Ucar, Y , Yagmurlu, N , Esen, A . "A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation". Politeknik Dergisi (2019): 443-451 <http://dergipark.org.tr/politeknik/issue/44136/428986>
Chicago Karaagac, B , Ucar, Y , Yagmurlu, N , Esen, A . "A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation". Politeknik Dergisi (2019): 443-451
RIS TY - JOUR T1 - A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation AU - Berat Karaagac , Yusuf Ucar , N. Murat Yagmurlu , Alaattin Esen Y1 - 2019 PY - 2019 N1 - doi: 10.2339/politeknik.428986 DO - 10.2339/politeknik.428986 T2 - Politeknik Dergisi JF - Journal JO - JOR SP - 443 EP - 451 VL - IS - SN - -2147-9429 M3 - doi: 10.2339/politeknik.428986 UR - https://doi.org/10.2339/politeknik.428986 Y2 - 2019 ER -
EndNote %0 Journal of Polytechnic A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation %A Berat Karaagac , Yusuf Ucar , N. Murat Yagmurlu , Alaattin Esen %T A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation %D 2019 %J Politeknik Dergisi %P -2147-9429 %V %N %R doi: 10.2339/politeknik.428986 %U 10.2339/politeknik.428986
ISNAD Karaagac, Berat , Ucar, Yusuf , Yagmurlu, N. Murat , Esen, Alaattin . "A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation". Politeknik Dergisi / (June 2019): 443-451. https://doi.org/10.2339/politeknik.428986