Numerical Method for Non-Stiff Differential Equations
The path of the trajectory of an aircraft from ground to space is modeled mathematically as a solution of the non-stiff differential equation. When the exact path is not tracable, we have to go for numerical solution of the model. To give optimal guidance to the aircraft, the path of the trajectory must be known. The need for the numerical method is to find the solution of a differential equation when the exact solution is not known. Traditionally, the order of convergence of the solution is proved theoretically and it can be tested with a test problem, if the exact solution is known. When the exact solution is not known, one cannot test the order of convergence of the numerical solution using the proved error estimates. In this paper, Euler method is applied to solve non-stiff differential equation when it does not have exact solution in hand, and an error estimate is derived to check the order of convergence of the solution of the numerical method. To show the behaviour of the numerical solution such as stability and order, in the complex plane, stability regions, order star, order star finger region, relative stability region, relative absolute region and order graph are presented. Experimental results are presented to show the performance of the numerical method with respect to the metrics such as regions of stability and theoretical and numerical rate of order of convergence of the solution, both numerically and graphically using MATLAB.
Aircraft trajectory path modelling, Non-stiff differential equation, Eulerâ€™s explicit method, Absolute error, Stability region.