Verification of Various Numerical Methods Using Hardware Implementation

Abstract

In Engineering there are some real systems which can be modeled mathematically with differential equations that can be solved using various numerical methods. Numerical methods are study of algorithms that use numerical approximation for the problems of mathematical analysis and control system. Moreover, there are many control algorithms required for controlling such systems like optimal control which requires Search Techniques to find local or global minima/maxima. These local or global minima/maxima can be obtained with the help of gradients and hessians. These gradients and hessians are calculated from numerical methods and basis on that decision can be made to select the suitable solver. These numerical algorithms are dedicated to applying its unique expertise in numerical software engineering to delivering high quality computational software and high performance computing services. In this project different numerical methods for ordinary differential equations are simulated for different system models. The system can be modeled using differential equations that are solved using available numerical methods. The comparative analysis has been carried out for different numerical methods using advanced software tools. The hardware implementation of the numerical methods has also been done using Real-Time (RT) embedded system/hardware. A Graphical User Interface (GUI) is developed for selection and comparison among the different numerical methods for the simulation as well as hardware implementation.