ODEASY: A query tool for ordinary differential equations.
|Title:||ODEASY: A query tool for ordinary differential equations.|
|Authors:||Tam, Kim M.|
|Abstract:||Ordinary differential equations (ODEs) are widely used in the modeling of physical systems. However, the numerical methods employed to approximate solutions to systems of ODEs can be constrained by truncation error, round-off error, and problems of stability and stiffness. These issues can be circumvented for equations that have known analytical solutions if the solutions are readily accessible in a database. The challenge then is to find a method of identifying an ODE given that it is unlikely that a query of the same ODE will have the equation elements presented in the same sequence and format by all users. Several possibilities of sorting equation elements are explored and an algorithm is developed and implemented which sorts the elements in order to convert the equation into a canonical form. The sorting algorithm explicitly defines this canonical form. By converting semantically identical equations into the same canonical form irrespective of the sequence of term entry, this algorithm is the basis of the development of ODEASY, the 'Ordinary Differential Equation Answer SYstem', which is a database system that accepts an ODE in any format for query. The input ODE is sorted to serve as its own index into the database of analytic solutions. ODEASY offers a sophisticated user interface for accessing the analytic solutions of ODEs of the first, second, and third order and of both the linear and nonlinear variety. ODEASY is a standalone PC system that also offers potential as a supporting tool to applications that provide a numerical approach to solving continuous system simulation.|
|Collection||Thèses, 1910 - 2010 // Theses, 1910 - 2010|