Fast and efficient algorithms for solving ordinary differential equations through computer algebra system

Abstract

Ordinary differential equations (ODE) occur in several branches of science and technology. One example may be study of particle interaction in electrorheological (ER) fluids. These are fluids whose properties change when they are exposed to an electric field. These fluids have important applications in many fields, automotive industries in particular. Calculations of interactions between particles suspended in fluid are carried out through the solution of ODE with regular singular point. Series solutions to such problems provide highly accurate results if a large number of terms in the series expansion are included. Based on this, several routines, to be used as a package in Computer Algebra System Maple®, are developed to solve the linear homogeneous ordinary differential equations with a regular singular point. These fast and efficient algorithms show significant improvements over existing routines in terms of memory and computational time requirements. The present algorithms provide the correct answer for many differential equations much more efficiently. Using these tools, a large number of terms in the series expansions can be included to get highly accurate solutions of ordinary differential equations.