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.

在本文中，我们构造了一个结合广义多项式混沌（gPC）表示和B样条小波的方案。首先，针对有界区间[0,1]构建半正交紧支撑的B样条小波，用于可能的随机过程的PC扩展。为了计算确定性的膨胀系数，我们将Galerkin投影应用于不确定数据和解变量。然后，为了确定随机过程的行为，使用四阶Runge-Kutta方法对从投影获得的方程组进行积分。为了处理非线性，我们将Galerkin投影与伪光谱投影进行了比较。通过现实生活中三个重要的模型问题来说明该过程。我们得出结论，与数值预期的伪谱方法相比，Galerkin逼近的性能更好。而且，已经观察到，与基于缩放函数的扩展相比，基于小波函数的扩展显示出优异的结果。