Solving economic models with heterogeneous agents requires computing aggregate dynamics consistent with individual behaviours. This paper introduces the finite volume method from the mathe-matics literature to enlarge the set of numerical methods available to compute dynamics in continuous time. Finite volume discretization methods allow theoretically consistent dimensional and local adaptivity that guarantee the mass conservation and positivity of the distribution function of the discretized system. This paper shows examples of 1) the Ornstein-Uhlenbeck process 2) the Aiyagari-Bewley-Huggett (wealth+income heterogeneity) model and 3) the lifecycle (wealth+income+age heterogeneity) model. The numerical exercises show that for the current dimensionality of the problems in economics, the finite volume method (with or without adaptivity) outperforms pre-existing methods. This paper further provides a companion open-source implementation of the finite volume method at github.com/sehyoun/adaptive_finite_volume to reduce the testing time of the finite volume method.