Some studies suggest a mathematical model as a way to reproduce the experiment and present a numerical solution of it, as shown in Figures 1 and 2. Figure 1 shows the experimental and numerical pattern formations of binary mixture [13].
Full Solution Numerical Analysis Burden 9th Edition 82l
Along with the study of mathematical model, various numerical schemes have been developed as a way to solve this accurately. At this time, a convergence test can be performed as a method for verifying the accuracy of such a numerical solution, which must be performed correctly.
This paper is structured in the following manner. In Section 2, we describe the numerical solution algorithms for the three equations. In Section 3, we present several numerical results. Then, in Section 4, we conclude.
The initial condition is on . We use = 1.0e-5, and . Because there is no analytic solution for (7), we consider a reference solution. We define the reference solution as the numerical solution with very fine space and time steps, (, ) = (3.81e-12, 1/2048).
We presented verification methods for the convergence rates of the numerical solutions for parabolic equations. As examples, we considered the numerical convergence rates of the heat equation, the AC equation, and the CH equation. Convergence test results showed that if we refine the spatial and temporal steps at the same time, then we may have the second-order convergence rate for the fully implicit scheme, which is first-order accurate in time and second-order accurate in space. Therefore, for a rigorous numerical convergence test, we need to perform the spatial and the temporal convergence tests separately.
However, the fact that the AEDPA burdens protected First Amendment rights is only the first step of the Court's analysis. Next the Court must determine to what extent the implicated activities are protected in order to determine the standard of review the Court should apply.
Plaintiffs' reliance on Massieu v. Reno, 915 F. Supp. 681, 698-703 (D.N.J.), rev'd on other grounds, 91 F.3d 416 (3d Cir.1996), to support their claim does not alter the Court's analysis. In Massieu, the court addressed the constitutionality of a statute which gave the Secretary the discretion to deport any alien lawfully within the United States, solely because the individual's presence in the United States would, in some unexplained way, impact the United States' foreign policy interests. Id. at 686.[27] The district court found the statute void for vagueness. Id. at 703. The court recognized that "neither the legislature nor the judiciary possesses the institutional competence to question the Secretary of State's decisions on matters of foreign policy." Id. at 701. Nevertheless, the Court stated that "`[f]oreign policy' cannot serve as the talisman behind which Congress may abdicate its responsibility to pass only sufficiently clear and definite laws when those laws may be enforced against the individual." *1203 Id. at 702 (citing Shahla v. INS, 749 F.2d 561, 563 n. 2 (9th Cir.1984)). 2ff7e9595c
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