Troesch denkleminin çözümü için Laguerre dalgacık yöntemi

Öz

Bu makalenin amacı lineer olmayan Troesch denklemini Laguerre dalgacık yöntemini kullanarak çözmektir.  Bilinmeyen fonksiyon Laguerre dalgacıkları ile yaklaştırılarak denklem bir cebirsel denklem sistemine dönüştürülür.  Bu yöntemin avantajlarından biri, lineer olmayan terimin lineer hale dönüştürülmesine gerek kalmamasıdır.  Denklem Troesch parametresinin farklı değerleri için çözülmüştür. Yöntemin etkin olduğunu göstermek için elde edilen sonuçlar gerek gerçek gerekse literatürdeki diğer sayısal sonuçlar ile karşılaştırılmıştır. 

Anahtar Kelimeler

• Laguerre dalgacık yöntemi,Troesch denklemi,Laguerre polinomu,Lineer olmayan diferensiyel denklem

Laguerre wavelet method for solving Troesch equation

Öz

The purpose of this paper is to illustrate the use of the Laguerre wavelet method in the solution of Troesch’s equation, which is a stiff nonlinear equation. The unknown function is approximated by Laguerre wavelets and the equation is transformed into a system of algebraic equations. One of the advantages of the method is that it does not require the linearization of the nonlinear term. The problem is solved for different values of Troesch’s parameter (μ) and the results are compared with both the analytical and other numerical results to validate the accuracy of the method.

Anahtar Kelimeler

• Laguerre Wavelet method,Troesch equation,Laguerre polynomial,Nonlinear differential equation

Kaynakça

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