Burgers ve coupled Burgers denklemlerinin tam ve nümerik çözümleri üzerine

Bu çalışmada, bir boyutlu Burgers denklemi ve Burgers denklemler sistemi Homotopi pertürbasyon metodu (HPM) ile çözülmüştür. Elde edilen çözümlerin iki ve üç boyutlu grafikleri ve tabloları Mathematica hesaplama programı yardımıyla oluşturulmuştur. Bu çalışmada bulunan tüm çözümler metodun etkinliğini doğrulamaktadır. Sonuçlara göre, elde ettiğimiz çözümlerin analitik çözümlere çok hızlı bir şekilde yakınsadığı ortaya çıkarılmıştır. Sonuç olarak, sunulan metodun geniş aralıktaki lineer olmayan problemlerin çözümleri için uygulanabilir olduğunu ifade etmemiz mümkündür.

Anahtar Kelimeler:

bir boyutlu Burgers denklemi, Coupled Burgers denklemi, Homotopi pertürbasyon metodu, yerleştirilen parametre

On Exact and Numerical Solutions to the Burgers' and Coupled Burgers' Equation

In this work, one dimensional Burgers' equation and coupled Burgers' equation are solved via Homotopy perturbation method (HPM). Solutions two and three-dimensional graphics and tables of some obtained results are constructed with the help of the computational program in the Wolfram Mathematica. All the solutions found in this study validate the efficiency of the method. According to the results, we have found out that our gained solutions convergence very speedily to the analytical solutions. In conclusion, we can say that the present method can also be applied for the solutions of a wide range of nonlinear problems.

Keywords:

one dimensional Burgers, Coupled Burgers, Homotopy perturbation method, embedding parameter,

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