Sentence examples for be the approximate solution from inspiring English sources

Let u be the solution of (2.4) and u h ∈ K h be the approximate solution of (3.1).

Let (u_{n}(x)) be the approximate solution of Eq. (4.1) in the space Ω and (u(x)) be the exact solution of Eq. (4.1).

Theorem 3.2 Let u ∈ K be solution of (2.5), and let u n + 1 be the approximate solution obtained from Algorithm  3.1.

Convergence verification: for a given small (varepsilon >0), if (| w^{k}-tilde{w}^{k}|_{infty}be the approximate solution.

Let (u_{i,j}^{n}) be the approximate solution at ((x_{i}, y_{j}, t_{n})), (u x,y,t)) represents the exact solution of (27).

(1) Let (epsilon> 0) and (phi_{n}) be the approximate solution of (1.1) such that (sup_{ninmathbb{Z}_Vert phi_{n+1}-Lambda _{n}phi_{n}Vert =sup_{ninmathbb{Z}_Vert e^{igamma(n+1)}xi (n+1)Vert ), (phi_{0}=theta_{0}), and (sup_{ninmathbb{Z}_Vert xi(n Vert leqepsilon), and let (theta_{n}) be the exact solution of (1.1).

Proof Let { u n } be the approximate solutions of problem (1.1 - 1.3) in the proof of Theorem 3.2, then (3.4) holds.

The starting point is the approximate solution for diffraction by a hard wedge given by Kouyoumjian and Pathak [1].

The blue line in Figure 2 is the approximate solution of (27) and the red line in Figure 2 is the approximate solution of (28).

Solid line represents the numerical solution to the full system, dotted line is the approximate solution.

The blue line in Figure 3 is the approximate solution of (29).