DIFF: Calculator for second and third order derivative computation

Abstract

Mühendislik eğitiminde sonlu fark yöntemleri uzun zamandır çalışma konusu olmasına rağmen, formülasyonlardaki iyileştirmeler hala ilgi konusudur. Bu bağlamda, bu yöntemlere dayalı hesap makinelerinin tasarımı önemli hale gelmektedir. Bu makalenin amacı, matematik problemlerinde herhangi bir fonksiyon için ikinci ve üçüncü dereceden türevleri hesaplayan bir hesap makinesi (DIFF) tasarlamaktır. DIFF, her türlü kullanıcı tarafından kullanılabilecek kadar kolay anlaşılan ve çok yönlü bir hesap makinesi olduğundan, bu amaç için bir platform olarak Matlab seçilmiştir. DIFF gömülü algoritması için Matlab Grafiksel Kullanıcı Arayüzü (GUI) ve Uygulamalarının her ikisinin de kullanılması ilk kezdir. Bu algoritma yalnızca Geri ve İleri sonlu fark yöntemlerini değil, aynı zamanda herhangi bir fonksiyonun ikinci ve üçüncü dereceden türevlerinin eş zamanlı olarak hesaplanması için geliştirilmiş İleri ve Geri sonlu fark yöntemleri gibi diğer teknikleri de içerir. DIFF'ten elde edilen her uygulama için sayısal sonuçlar ve ekran görüntüleri sunulmaktadır.

Keywords

• Sonlu fark yöntemleri
• Geliştirilmiş sonlu fark yöntemleri
• Matlab
• DIFF.

DIFF: Calculator for second and third order derivative computation

Abstract

Although finite difference methods in engineering education have been the subject of the study for a long time, the improvement in formulations is still object of interest. In this context, design of calculators based on these methods becomes important. The aim of this article is to design a calculator (DIFF) which computes second and third order derivatives for any functions in parts of mathematics problems. Any kind of user can use DIFF conveniently because of its versatility and easy-to-understand property. MATLAB is selected as a platform for this purpose. It is the first time that MATLAB Graphical User Interface (GUI) and Apps are both used for algorithm embedded in DIFF. This algorithm includes not only Backward and Forward finite difference methods but also other techniques such as improved Forward and Backward finite difference methods for computation of second and third order derivatives of any functions, concurrently. Numerical results and screenshots for each application obtained from DIFF are presented.

Keywords

• Finite difference methods
• Improved finite difference methods
• Matlab
• DIFF.

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