Investigating a hybrid perturbation-Galerkin technique using computer algebra

Investigating a Hybrid Perturbation-Galerkin Technique Using Computer Algebra

Nonresonant Excitation of the Forced Duffing Equation

We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

Computer Algebra Technique for Abrasive Treatment Process Dynamics

The mathematical model was compiled for the studies of the dynamics of an abrasive processing in a magnetic field. An analytical solution of its nonlinear part was found synthesizing harmonic balance method and computer algebra technique. Solutions of the linear part were obtained by the traditional numerical techniques. The numeric investigation of process dynamic features was fulfilled, regim...

Teaching Commutative Algebra and Algebraic Geometry using Computer Algebra Systems

In teaching a mathematics course in commutative algebra and algebraic geometry, we would like to equip students with a computer algebra system so they can solve problems that they might encounter in their own research or in industry. The purpose of this paper is to firstly describe how we use computer algebra in the course that we teach and secondly, to share with the reader a list of applicati...

A Computer Algebra System

Systems of polynomial equations appear throughout mathematics, science, and engineering, but solving them is widely considered to be part of numerical analysis, not computer algebra or algebraic geometry. Due to rounding errors, though, purely numerical methods often are unstable in unpredictable ways. They usually don’t find all solutions and frequently have problems with overdetermined system...