Sentence examples for smooth solution and from inspiring English sources
Consequently, if building simulation programs are built on models that satisfy the smoothness assumptions required to prove existence of a unique smooth solution, and if their numerical solvers allow controlling the approximation error, one can use such programs with generalized pattern search optimization algorithms that adaptively control the precision of the solutions of the DAE system.
The method converges fast to a smooth solution, and the resulting horn has good impedance properties throughout the entire frequency band of interest.
Our new stabilized methods are L∞ stable, second order accurate for any smooth solution and with accuracy of order 2/3 for solutions with moving discontinuities.
However, these methods do not always produce a smooth solution and often result in an estimate of (mu (t)) that is wiggly, indicating overfit to the data.
We consider the sublevel sets I θ ⊂ I − ϵ ⊂ I ϵ ⊂ E. Suppose that 0 and v 0 are the only critical points of I. Otherwise, we have a second nontrivial smooth solution and so we are done.
We first show the accuracy of the scheme in the case of a smooth solution and measure rigorously its convergence order so as to show that the entropy-driven limiter does not spoil the convergence properties of the high-order method upon which it is built.
The method is designed for problems with smooth solutions, and is based on a multidomain spectral collocation discretization scheme.
we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions.
Several numerical examples are computed to validate the numerical accuracy, effectiveness and robustness of the present method for TFADEs with smooth solutions and different boundary conditions.
Various numerical examples are presented and the hybrid algorithm is proved to be accurate for smooth solutions and be able to capture discontinuities robustly.
The overall FSI-DCG scheme is shown to be second-order accurate in the max-norm for smooth solutions, and robust and stable for problems with discontinuous solutions for a wide range of constitutive parameters.
