Ömür Kıvanç KÜRKÇÜ, Duygu DÖNMEZ DEMİR, Tuğçe ÇINARDALI, Mehmet SEZER

Fizik ve Mekanikte Ortaya Çıkan Bazı Lineer Olmayan Diferansiyel Denklemler için Legendre Matris-Kollokasyon Yaklaşımı

Bu çalışmada, fizik ve mekanikte ortaya çıkan lineer olmayan bazı terimlere sahip yüksek mertebeden adi diferansiyel denklemlerin çözümü için, kollokasyon noktalarına dayanan operasyonel Legendere matris metodu takdim edilmiştir. Bu teknik, karışık koşullar sayesinde, bilinmeyen Legendre katsayıları ile lineer olmayan bir diferansiyel denklemi bir matris denklemine dönüştürür. Bu matris denkleminin çözümü, çözüm fonksiyonunun Legendre katsayılarını verir. Böylece, yaklaşık çözüm Legendre polinomları cinsinden elde edilir. Yöntemin faydasını ve uygulanabilirliğini göstermek için, rezidüel hata tahmini ile birlikte bazı test problemleri verilir ve nümerik sonuçlar kıyaslanır.

The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics

In this study, the Legendre operational matrix method based on collocation points is introduced to solve high order ordinary differentialequations with some nonlinear terms arising in physics and mechanics. This technique transforms the nonlinear differential equationinto a matrix equation with unknown Legendre coefficients via mixed conditions. This solution of this matrix equation yields theLegendre coefficients of the solution function. Thus, the approximate solution is obtained in terms of Legendre polynomials. Some testproblems together with residual error estimation are given to show the usefulness and applicability of the method and the numericalresults are compared.

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