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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2024 / Volume: 73 Issue: 4

The dependency of the analytical and numerical solution on the $\varepsilon$ parameter in hyperbolic and pseudo-hyperbolic problems with inverse coefficients

Akbala Yernazar(KOCAELI UNIVERSITY)0000-0002-0068-4954
Erman Aslan(KOCAELI UNIVERSITY)0000-0001-8595-6092
İrem Bağlan(KOCAELI UNIVERSITY)0000-0002-1877-9791
Sayfa
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Yayın Tarihi
2024-12-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The cases where $\varepsilon =0$ and $\varepsilon \neq 0$ have been solved analytically and numerically, and compared each other.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The aim of this study is to analyze the behavior of $\varepsilon$ on the solution of an inverse coefficient nonlinear pseudo-hyperbolic equation $w_{tt}-\varepsilon w_{xxtt}-\varepsilon w_{xx}=\theta (t)f(x,t,w)$ with periodic boundary conditions.
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Temel Bulgular & Veri:We also consider the inverse coefficient problem $w_{tt}-w_{xx}=\theta (t)f(x,t,w).$ The solution function of nonlinear pseudo-hyperbolic equation is found to be convergent to the solution function of nonlinear hyperbolic equation, when $ \varepsilon \rightarrow 0$ is proved.
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Sonuç & Katkı:The cases where $\varepsilon =0$ and $\varepsilon \neq 0$ have been solved analytically and numerically, and compared each other.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Nonlinear pseudo-hyperbolic equation · inverse coefficient problem · periodic boundary condition

Abstract

The aim of this study is to analyze the behavior of $\varepsilon$ on the solution of an inverse coefficient nonlinear pseudo-hyperbolic equation $w_{tt}-\varepsilon w_{xxtt}-\varepsilon w_{xx}=\theta (t)f(x,t,w)$ with periodic boundary conditions. We also consider the inverse coefficient problem $w_{tt}-w_{xx}=\theta (t)f(x,t,w).$ The solution function of nonlinear pseudo-hyperbolic equation is found to be convergent to the solution function of nonlinear hyperbolic equation, when $ \varepsilon \rightarrow 0$ is proved. The Fourier method was used to illustrate the theoretically relation between the inverse problems while the Finite Difference Method was used numerically. In order to get more accurate numerical solution higher precision schemes have been applied in implicit finite difference equation. The cases where $\varepsilon =0$ and $\varepsilon \neq 0$ have been solved analytically and numerically, and compared each other.

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Bu Makaleye Atıf Yap

Yernazar, A., Aslan, E., Bağlan, İ. (2024). The dependency of the analytical and numerical solution on the $\varepsilon$ parameter in hyperbolic and pseudo-hyperbolic problems with inverse coefficients. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 4. https://doi.org/10.31801/cfsuasmas.1475286

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