A quadratic spline projection method for computing stationary densities of random maps

Abstract

We propose a quadratic spline projection method that computes stationary densities of random maps with position-dependent probabilities. Using a key variation inequality for the corresponding Markov operator, we prove the norm convergence of the numerical scheme for a family of random maps consisting of the Lasota–Yorke class of interval maps. The numerical experimental results show that the new method improves the $L^1$-norm errors and increases the convergence rate greatly, compared with the previous operator-approximation-based numerical methods for random maps.