الفهرس 
Uncertainty quantification and propagation
Singularly perturbation problemsSingularly perturbation problemsOnly 14 pages are availabe for public view
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Abstract
numerical methods have been developed for two types of problems i. Random differential equations. ii. Singularly perturbed boundary value problems with random parameters. For the random differential equations, a numerical technique has been developed for estimating the solution for both linear and nonlinear problems which exhibits uncertain parameters- in different engineering fields (structure, electrostatic and fluid mechanics). The proposed method is based on polynomial chaos expansion (PCE) and exponential spline scheme, which makes the method more efficient than the traditional methods. The Monte Carlo simulations (MCS) are used as a validating tool to verify the applicability and the accuracy of the developed method. The developed technique was applied on illustrative examples – uncertainty quantification of beam deflection. Beam deflection statistics have been estimated in two cases; when there is a random load applied on the beam and the second case when the beam material has random elasticity. In each case, the deflection has been estimated and its statistical moments such as the mean and the standard deviation. The proposed approach is shown to be more accurate and converge faster than the classical PCE technique and it has a second-order accuracy.