The convergence estimates for Galerkin-wavelet solution of periodic pseudodifferential initial value problems.

Nguyen Minh Chuong; Bui Kien Cuong

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For a class of anisotropic integrodifferential operators $ℬ$ arising as semigroup generators of Markov processes, we present a sparse tensor product wavelet compression scheme for the Galerkin finite element discretization of the corresponding integrodifferential equations $ℬ$ on [0,1] with possibly large . Under certain conditions on $ℬ$ , the scheme is of essentially optimal and dimension independent complexity $𝒪$ ( | log |) without corrupting the convergence...