Lineer olmayan kısmi türevli denklemlerin homotopi pertürbasyon tekniği ile çözümleri
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Date
2015
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Niğde Üniversitesi / Fen Bilimleri Enstitüsü
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info:eu-repo/semantics/openAccess
Abstract
Lineer olmayan kısmi türevli Drinfield-Sokolov-Wilson, Drinfield-Sokolov ve Modifiye- Benjamin-Bona-Mahony denklemlerinin çözümleri homotopi pertürbasyon tekniği kullanılarak elde edilmiştir. Drinfield-Sokolov-Wilson denklem sisteminin pertürbatif çözümü için yalnızca bir iterasyon yapılmış, Drinfield-Sokolov ve ModifiyeBenjamin-Bona-Mahony denklemlerinin pertürbatif çözümleri için ise altı iterasyona kadar gidilmiştir. Elde edilen bazı çözümlerin davranışı ve nümerik farkları grafiklerle de sunulmuştur. Ayrıca, bu denklemler için birinci iterasyonlardan elde edilen pertürbatif çözümler kullanılarak basit dallanma noktaları tespit edilmiştir
The analytic solutions of the nonlinear partial differantial equations, Drinfield-SokolovWilson, Drinfield-Sokolov and Modified-Benjamin-Bona-Mahony equations are obtained by using the homotopy perturbation technique. While only one iteration is performed for the perturbative solution of Drinfield-Sokolov-Wilson esystem, we have shown the perturbative solutions upuntil six iterations for Drinfield-Sokolov and Modified-Benjamin-Bona-Mahony equations. The behavior of the some of the solutions and their numerical differences are presented via graphics. Moreover, simple bifurcation points are noticed by using the obtained perturbative solutions of these equations computed from first iteration.
The analytic solutions of the nonlinear partial differantial equations, Drinfield-SokolovWilson, Drinfield-Sokolov and Modified-Benjamin-Bona-Mahony equations are obtained by using the homotopy perturbation technique. While only one iteration is performed for the perturbative solution of Drinfield-Sokolov-Wilson esystem, we have shown the perturbative solutions upuntil six iterations for Drinfield-Sokolov and Modified-Benjamin-Bona-Mahony equations. The behavior of the some of the solutions and their numerical differences are presented via graphics. Moreover, simple bifurcation points are noticed by using the obtained perturbative solutions of these equations computed from first iteration.
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Homotopi Pertürbasyon Metodu, Dallanma Noktası, Drinfield-Sokolov-Wilson Denklemi, Drinfield-Sokolov Denklemi, Benjamin-Bona-Mahony Denklemi, Homotopy Perturbation Method, Bifurcation Point, Drinfield-Sokolov-Wilson Equation, Drinfield-Sokolov Equation, Modify- Benjamin-Bona-Mahony Equation
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Mart, H.Y. (2015). Lineer olmayan kısmi türevli denklemlerin homotopi pertürbasyon tekniği ile çözümleri. (Yüksek lisans Tezi). Niğde Ömer Halisdemir Üniversitesi, Fen Bilimleri Enstitüsü, Niğde
