Adaptive Wavelet Methods on Unbounded Domains

In this paper, we introduce an adaptive wavelet method for operator equations on unbounded domains. We use wavelet bases on R to equivalently express the operator equation in terms of a well-conditioned discrete problem on sequence spaces. By realizing an approximate adaptive operator application also for unbounded domains, we obtain a scheme that is convergent at an asymptotically optimal rate. We show the quantitative performance of the scheme by various numerical experiments.