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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 1

A new operational approach for solving weakly singular integro-differential equations

Khadijeh SADRİ
Zainab AYATİ
Sayfa
107–127
Yayın Tarihi
2018-02-01
DOI
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It is further found that the absolute errors are almost constant in the studied interval.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Based on Jacobi polynomials, an operational method is proposed to solve weakly singular integro–differential equations.
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Temel Bulgular & Veri:These equations appear in various fields of science such as physics and engineering, the motion of a plate in a viscous fluid under the action of external forces,problems of heat transfer, and surface waves.
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Sonuç & Katkı:It is further found that the absolute errors are almost constant in the studied interval.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Singular integro–differential equations · Shifted Jacobi polynomials · Operational matrices of integration and product

Abstract

Based on Jacobi polynomials, an operational method is proposed to solve weakly singular integro–differential equations. These equations appear in various fields of science such as physics and engineering, the motion of a plate in a viscous fluid under the action of external forces,problems of heat transfer, and surface waves. To solve the weakly singular integro–differential equations, a fast algorithm is used for simplifyingthe problem under study. The Laplace transform and Jacobi collocation methods are merged, and thus, a novel approach is presented. Some theorems are given and established to theoretically support the computational simplifications which reduce costs. In order to show the efficiency and accuracy of the proposed method some numerical results are provided. It is found that the proposed method has lesser computational size compared to other common methods, such as Adomian decomposition, Taylor expansion, and Bernstein operational methods. It is further found that the absolute errors are almost constant in the studied interval.

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Bu Makaleye Atıf Yap

SADRİ, K., AYATİ, Z. (2018). A new operational approach for solving weakly singular integro-differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 1, 107–127. https://ajindex.com/articles/669447

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