@article{Schiffman:333479,
      recid = {333479},
      author = {Schiffman, Florian},
      title = {Runge-Kutta integrators for fast and accurate solutions in  GEMPACK},
      address = {2022},
      pages = {14},
      year = {2022},
      note = {Presented at the 25th Annual Conference on Global Economic  Analysis (Virtual Conference)},
      abstract = {In GEMPACK, models are always solved as initial value  problems(IVP)using the linearized form of the levels  equations. While this allows the user to solve each step of  the IVP efficiently, the overall accuracy and speed is  determined by the integration scheme and the number of  integration steps. Up to GEMPACK 12.1, only the Euler,  leapfrog midpoint and Gragg’s method were available as well  as their 2 and 3 point Richardson extrapolations. While  Euler provides excellent stability it is very costly to  obtain accurate solutions. In contrast the latter two  integrators allow for faster convergence but oftentimes  suffer from instabilities. In the current beta version of  GEMPACK we address this issue by introducing explicit and  embedded Runge Kutta (RK) integrators as an alternative.  Our focus in this work is on the embedded RK methods. Using  the embedded RK methods we developed a new adaptive step  size algorithm that is designed to overcome problem common  to CGE models. Such problems include asymptotes in the  levels variables as well as coping with the different  scales on which the results can vary. Our algorithm  provides rapid convergence towards the true solution as  well as increased robustness exceeding that of Eulers  method. In addition, the new algorithm allows us to provide  users with a component-by-component global error estimate.  In all our tests we have found that the error estimates  appeared to be upper bounds of the true error. Furthermore,  this compenent-by-component error estimates are an  excellent debugging tool when developing or extending a CGE  model.In all but the simplest test cases, we have found  that using adaptive step size embedded RK methods provided  solutions at least one order of magnitude closer to the  true solution in less than half the time to solution  required by the old integration schemes.},
      url = {http://ageconsearch.umn.edu/record/333479},
}