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Dergiler / Politeknik Dergisi / 2019 / Cilt: 22 - Sayı: 2

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

Berat KARAAGAC
Yusuf UÇAR
N. Murat YAĞMURLU
Alaattin ESEN
Sayfa
443–451
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The newly calculated error norms show that numerical results are in a good agreement with the exact solutions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In the present manuscript, a new numerical scheme is presented for solving the time fractional nonlinear Klein-Gordon equation.
📊
Temel Bulgular & Veri:The approximate solutions of the fractional equation are based on cubic B-spline collocation finite element method and L2 algorithm.
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Sonuç & Katkı:The newly calculated error norms show that numerical results are in a good agreement with the exact solutions.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Finite element method · collocation · Fractional Klein Gordon equation

Özet

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.

Abstract

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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Bu Makaleye Atıf Yap

KARAAGAC, B., UÇAR, Y., YAĞMURLU, N. M., ESEN, A. (2019). A New Perspective on The Numerical Solution for Fractional Klein Gordon Equation. Politeknik Dergisi, Cilt: 22 - Sayı: 2, 443–451. https://ajindex.com/articles/307056

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Kaynakça (13)

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