Sentence examples for for smooth solutions from inspiring English sources

For smooth solutions, Eqs.

The results show exponential error convergence of order p + 1∕2 for smooth solutions.

Especially for smooth solutions, the qualities (1.2). are all time independent [18].

Numerical experiments demonstrate the expected high spectral accuracy for smooth solutions.

The resulting PDEs are then discretized by existing classical numerical methods on a regular grid for smooth solutions.

The method is third-order accurate in time and converges exponentially fast in space for smooth solutions.

end{aligned} Therefore, the conclusion of this lemma is true for smooth solution (u x,t)).

We implement an error indicator and a shock identifier to capture shocks with slope-limited linear elements, while using high-order Legendre polynomials for smooth solution regions.

A Beale-Kato-Majda type blow-up criterion for smooth solution to (1.1) that relies on the vorticity of velocity only is obtained by Yuan [7].

A BKM type blow-up criterion for smooth solution that relies on the vorticity of velocity only was obtained by Yuan [7].

This paper is devoted to the rigorous justification of the convergence of the above low Froude number limit for smooth solution of the inviscid rotating Euler and shallow water equations in a bounded two-dimensional domain Ω.