Diferansiyel Denklemler İçin Matlab Kullanarak Nümerik Çözümler

Yıl 2025, Cilt: 41 Sayı: 2, 616 - 630, 30.08.2025

Bengü Çına

Öz

Diferansiyel denklemlerin fizik, mühendislik, biyoloji ve ekonomi gibi disiplinlerdeki bir dizi olgunun modellenmesindeki rolü büyük önem taşımaktadır. Birçok diferansiyel denklem analitik olarak çözülebilmesine rağmen, diğerleri bu konuda bir zorluk teşkil etmektedir. MATLAB, bu karmaşık denklemlerin çözümünü kolaylaştırmak için kullanılabilir. Bu çalışmanın amacı, analitik çözümü olmayan veya çözümü karmaşık olan diferansiyel denklemlerin MATLAB kullanılarak sayısal çözümlerini elde etmek ve bu çözümlerin grafiklerini analiz etmektir. Bu sayede denklemlerin dinamik davranışları ve çözüm aralıkları hakkında daha derin bir anlayış kazanmayı hedefliyoruz. Bu amaçla çoğunlukla ode45 fonksiyonu ve Runge-Kutta yöntemi kullanılacaktır.

Anahtar Kelimeler

Ode45 , Runge-Kutta Yöntemi , Dormand-Prince (4 , 5) , Matlab.

Numerical Solutions for Differential Equations Using Matlab

Öz

The role of differential equations in modelling a range of phenomena across disciplines, including physics, engineering, biology and economics, is of great significance. Despite many differential equations can be solved analytically, others present a challenge in this regard. MATLAB can be employed to facilitate the resolution of these intricate equations. The aim of this study is to obtain numerical solutions of differential equations that have no analytical solutions or whose solutions are complex using MATLAB and to analyse the graphs of these solutions. In this way, we aim to gain a deeper understanding of the dynamic behaviour of the equations and their solution ranges. For this purpose, the ode45 function and the Runge-Kutta method will be mostly used.

Anahtar Kelimeler

Ode45 , Runge-Kutta method , Dormand-Prince (4 , 5) Method , Matlab.

Kaynakça

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• https://doi.org/10.38016/jista.1447980