Application of Perturbation Methods to Approximate the Solutions to Static and Non-linear Oscillatory Problems FINAL

Overview of Work Linear ODE – Found Regular Perturbation Solution Duffing – Found Regular and Poincare- Lindstedt method ( to eliminate secular term) Van Der Pol – Found Regular and Multiple Scales solution ( to eliminate the secular term). Poincare Lindstedt method failed at given boundary conditions

Linear ODE

Duffing equation Case 1: ε =.01

Duffing equation Case 2: ε =.05

Van der Pol Case 1: ε =.01

Van der Pol Case 2: ε =.05