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The computational interval can be transformed from [0, 1] to [a, b] via an affine transformation.
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High accuracy in long computational intervals and the stability of the approximated solutions encourage us to apply a similar method for solving other applied mathematics problems (see, for instance, [31]) in the future.
The proposed strategy knocks down the computational barrier of computing interval failure probabilities, and reduces the cost of a robust reliability analysis by many orders of magnitude.
Our algorithm implements this dielectric model, which in the time-domain involves fractional derivatives and fractional differential operators, with a preset error over the desired computational time interval [0,Tcomp] and correctly takes into account the singularity at t = 0+ of the corresponding time-domain dielectric susceptibility.
The computational time interval is 0.6 s to satisfy the stability condition of the finite difference method.
The computational time interval Δt is 1.0 × 10−3 s, The maximum permissible error of the continuity equation Dmax is 1.0 × 10−5, fluid density ρ is 1.0 × 103 kinematicnematic viscosity ν is 1.0 × 10−6 m2/s, density of the driftage ρ d is 0.5 × 103 kg/m3, and the reflection coefficient between the driftage and vertical wall e is 0.5.
The computational confidence intervals were calculated using the Monte Carlo method.
The model was validated by comparing sample paths and computational confidence intervals with three experimental data sets of a tubular milli-reactor for polystyrene production with different configurations.
A new hybrid probabilistic and interval computational scheme is proposed to robustly assess the stability of engineering structures involving mixture of random and interval variables.
To reduce the computational cost, the interval arithmetic is introduced in the inner loop to improve computational efficiency without compromising numerical accuracy.
A new hybrid probabilistic and interval computational method is proposed for robustly assessing both time-dependent serviceability and strength limit of concrete-filled steel tubular arch structures involving both random and interval variables.
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