Abstract
In this paper, we have constructed a scheme combining generalized Polynomial Chaos (gPC) representation and B-spline wavelets. To begin with, semi-orthogonal compactly supported B-spline wavelets are constructed for the bounded interval [0,1] which are used for PC expansion of possible stochastic processes. To compute the deterministic coefficients of expansion, we have applied Galerkin projection on uncertain data and the solution variables. Then, to ascertain the behavior of the random process, the system of equations obtained from projection are integrated using fourth order Runge–Kutta method. To handle the nonlinearity, we have compared Galerkin projection with pseudo-spectral projection. The procedure is illustrated through three model problems of real life importance. We conclude that Galerkin approximation performs better in comparison to pseudo-spectral approach which is numerically expected. Also, it has been observed that the wavelet function based expansion shows superior results as compared to scaling function based expansion.
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