Method for reduced basis discovery in nonstationary problems

Model reduction methods allow to significantly decrease the time required to solve a large ODE system in some cases by performing all calculations in a vector space of significantly lower dimension than the original one. These methods frequently require apriori information about the structure of the solution, possibly obtained by solving the same system for different values of parameters. We suggest a simple algorithm for constructing such a subspace while simultaneously solving the system, thus allowing one to benefit from model reduction even for a single system without significant apriori information, and demonstrate its effectiveness using the Smoluchowski equation as an example.