ODEs 3

• Write the following 3rd order ODE as three first order ODEs: $gg^{\prime\prime} + 2g^{\prime\prime\prime} = 0$
• Show how to use an eigenvector decomposition to decouple a system of linear ODEs.
• Show how to verify the order of an ODE method by changing the step size and plotting/fitting
• What are two approaches to using automatic, variable step sizes for ODE methods?
  • Write down the equation for modifying the step size.
• For the two reaction system $A+B\rightarrow C$ and $A+C\rightarrow D$ with rate constants $k_1$ and $k_2$, write the system of ODEs.
  • Is this system linear or nonlinear?
• Write down the advancement formulas for the 4th order RK method.