Identifying Stiff Ordinary Differential Equations and Problem Solving Environments (PSEs)
B. K. Aliyu *
Federal Ministry of Science and Technology (FMST), National Space Research and Development Agency (NASRDA), Centre For Space Transport and Propulsion (CSTP) Epe, Lagos State, Nigeria.
C. A. Osheku
Federal Ministry of Science and Technology (FMST), National Space Research and Development Agency (NASRDA), Centre For Space Transport and Propulsion (CSTP) Epe, Lagos State, Nigeria.
A. A. Funmilayo
Federal Ministry of Science and Technology (FMST), National Space Research and Development Agency (NASRDA), Centre For Space Transport and Propulsion (CSTP) Epe, Lagos State, Nigeria.
J. I. Musa
Federal Ministry of Science and Technology (FMST), National Space Research and Development Agency (NASRDA), Centre For Space Transport and Propulsion (CSTP) Epe, Lagos State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Stiff Ordinary Differential Equations (SODEs) are present in engineering, mathematics, and sciences. Identifying them for effective simulation (or prediction) and perhaps hardware implementation in aerospace control systems is imperative. This paper considers only linear Initial Value Problems (IVPs) and brings to light the fact that stiffness ratio or coefficient of a suspected stiff dynamic system can be elusive as regards the phenomenon of stiffness. Though, it gives the insight suggesting stiffness when the value is up to 1000 but is not necessarily so in all ODEs. Neither does a value less than 1000 imply non-stiffness. MATLAB/Simulink® and MAPLE® were selected as the Problem Solving Environment (PSE) largely due to the peculiar attribute of Model Based Software Engineering (MBSE) and analytical computational superiority of each PSEs, respectively. This creates the base for comparing results from both numerical and analytical standpoint. In Simulink, two methods of modelling ODEs are presented. Experimenting with all the variable-step solvers in MATLAB® ODE Suit for selected examples was carried out. Results point to the fact that stiffness coefficient of about 1000does not always suggest that an ODE is stiff nor does a value less than 1000 suggest non-stiff.
Keywords: ODEs, stiffness ratio, MATLAB/Simulink®, MAPLE®, variable-step solvers.