Software to help solve mathematical models

This week, University Putra Malaysia's team unveiled their latest inventions and products at the 34th International Exhibition of Inventions, New Techniques and Products in Geneva (April 2-6, 2008), also known as the World's Largest Market-Place for Inventions.

This research is on a software to solve 2nd and 3rd order ordinary differential equations without modifying the structure of the problem tested i.e. not reducing it to the first order system. The code is useful to the scientist, engineers, applied mathematicians and educators to solve many mathematical models in the form of higher order ordinary differential equations in various areas including physics, chemistry, biology, engineering and economics.

TITLE: Direct Block Software for Solving Higher Order Ordinary Differential Equations

RESEARCHERS: Dr. Zanariah Abdul Majid and Prof. Dato’ Dr. Mohamed Suleiman

Contact details for Dr. Zanariah Abdul Majid
Department of Mathematics,
Faculty of Science,
Universiti Putra Malaysia,
43400 UPM Serdang,
Selangor Darul Ehsan, Malaysia
Tel: 03-89467959
Fax: 03-894377958
Email: zanariah@science.upm.edu.my
A structured and efficient algorithm of the new block method is developed for solving directly the second and third order system of ordinary differential equations (ODEs) using variable step size. This code will estimate the solutions of initial value problems at two points simultaneously in a block and therefore it may produce faster numerical results.

The higher order ODEs can be solved by reducing it to a system of first order ODEs and then solved using any numerical method i.e Euler method. This approach is very well established but it obviously will enlarge the system of first order ODEs. However, the developed code will solve the higher order ODEs directly without reducing it to the first order system. The aim is to solve the higher order ODEs as it appears and never modify the structure of the problem tested.

The code is suitable for solving the numerical integration of non stiff and mildly stiff higher order differential systems. The numerical results obtained are very efficient in terms of accuracy and timing. The source code developed would be useful to the scientist, engineers, applied mathematicians and educators to solve many mathematical models in the form of higher order ordinary differential equations in various areas including physics, chemistry, biology, engineering and economics.