Sentence examples for between the true solution from inspiring English sources
In short, the derivation of (1.2) is based on the local truncated error analysis and the error correction term comes from a certain approximation of the difference between the true solution of SDEs and one-step explicit Milstein approximation.
The aim of this paper is to investigate the rate of approximation between the true solution and the numerical solution in the sense of the L p -norm when the drift and diffusion coefficients are Taylor approximations.
Remark From the proof, we can easily understand that the convergence speed between the true solution of Eq. (1) and the approximation solution is faster than the Euler-Maruyama method.
For better visualization of these solutions we consider the differences between these solutions and the true solution in Fig. 6.
Finally, a new external index called correlation index (CI), which considers the correlation relationship of both the similarity and dissimilarity between the predicted solution and the true solution, is proposed to evaluate the performance of BSEA.
Results for first-order and LHHW kinetics show good agreement between the one-dimensional approximation and the true solution.
This approach offers practical perspectives in that it enables us to control the error, on each subdomain between the discrete Schwarz algorithm and the true solution.
Hence, the true solution υ, which lies in between, must converge uniformly to w and the proof of (ii) is completed.
Since the vH solution was closer to the true solution than the VV and HH solutions, the difference between the true and the vH solutions in Fig. 6 was plotted in order to demonstrate that the combined solution 1 is a solution between the simple mean and the VH solution; however, as can be seen, the combined solution 2 is even superior to the VH solution.
The true solution is u(x) = sin(πx) + 1.
