Various techniques to solve Blasius equation

Abstract

This paper presents three distinct approximate methods for solving Blasius Equation. The first method can be regarded as an improvement to a series solution of Blasius by means of Padè approximation. The second method is a famous type of weighted residual technique which is called Galerkin method after the famous Russian engineer and mathematician Boris Galerkin. The last method is a simple discrete, numerical technique. Additionally, in order to show the power of the last method, the Thomas-Fermi problem is solved using the same technique. Results obtained by all three methods are highly accurate in comparison with the Howarth’s solution and Bender’s solution.

Keywords

• Blasius equation,perturbation technique,Padè approximation,weighted residual method,Galerkin method,Thomas Fermi equation

Blasius denkleminin çözümü için çeşitli teknikler

Abstract

Bu makalede Blasius Denklemi’ni çözmek için üç farklı yaklaşık yöntem sunmaktadır. İlk yöntem Blasius’un seri çözümünün Padè yaklaşımı yardımı ile iyileştirilmesi olarak değerlendirilebilir. İkinci yöntem ünlü Rus mühendis ve matematikçi Boris Galerkin’e izafeten Galekin Metodu olarak adlandırılan bir ağırlıklı artık yöntemdir. Son yöntem ise basit, ayrık bir sayısal tekniktir. Ek olarak son yöntemin gücünü göstermek adına Thomas-Fermi Problemi de aynı teknik ile çözülmüştür. Her üç yöntem, sonuçlar Howarth’ın ve Bender’in çözümü ile kıyaslandığında, oldukça başarılı sonuç vermektedir.

Keywords

• Blasius denklemi,pertürbasyon tekniği,Padè yaklaşımı,ağırlıklı artık yöntemler,Galerkin metodu,Thomas Fermi denklemi

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