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In this paper, a novel method to adaptively approximate the solution tostochastic differential equations, which is based on compressive sampling andsparse recovery, is introduced. The proposed method consider the problem ofsparse recovery with respect to multi-wavelet basis (MWB) from a small numberof random samples to approximate the solution to problems. To illustrate therobustness of developed method, three benchmark problems are studied and mainstatistical features of solutions such as the variance and the mean ofsolutions obtained by proposed method are compared with the ones obtained fromMonte Carlo simulations.

A Compressive Sampling Approach To Adaptive Multi-Resolution Approximation of Differential Equations With Random Inputs