Two initial boundary value problems, one having analytical solution and the other is set up with a non analytical initial condition, have been simulated by the proposed method.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:The extended form of the classical polynomial cubic B-spline function is used to set up a collocation method for some initial boundary value problems derived for the Korteweg-de Vries-Burgers equation.
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Temel Bulgular & Veri:Having nonexistence of third order derivatives of the cubic B-splines forces us to reduce the order of the term uxxx to give a coupled system of equations.
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Sonuç & Katkı:Two initial boundary value problems, one having analytical solution and the other is set up with a non analytical initial condition, have been simulated by the proposed method.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Özet
The extended form of the classical polynomial cubic B-spline function is used to set up a collocation method for some initial boundary value problems derived for the Korteweg-de Vries-Burgers equation. Having nonexistence of third order derivatives of the cubic B-splines forces us to reduce the order of the term uxxx to give a coupled system of equations. The space discretization of this system is accomplished by the collocation method following the time discretization with Crank-Nicolson method. Two initial boundary value problems, one having analytical solution and the other is set up with a non analytical initial condition, have been simulated by the proposed method.
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Bu Makaleye Atıf Yap
HEPSON, Ö. E., KORKMAZ, A., DAĞ, I. (2019). EXTENDED B-SPLINE COLLOCATION METHOD FOR KDV-BURGERS EQUATION. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 9 - Sayı: 2, 267–278. https://ajindex.com/articles/327624
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