Sentence examples for between exact and numerical from inspiring English sources

The results show a very good match between exact and numerical solutions.

In Table 6, the maximum errors and convergence orders in spatial directions with (tau=10^{-4}) and (tin[0,0.01]) are listed, whereas in Figures 5-6, comparison between the exact and numerical solutions is shown under certain conditions.

Comparison between the exact and numerical solutions and the approximating errors under different conditions are shown in Figures 3-4, whereas the maximum errors and convergence orders in spatial directions with (tin[0,0.1]) are listed in Tables 3 and 4. Figure 3 Errors with (pmb{h=1/40}) ; (pmb{h=1/40}1}) ; (pmb{h=1/40}.5}).

In order to investigate the convergence of the finite difference scheme (9), let (varepsilon_{i}^{n}=U_{i}^{n}-u_{i}^{n}, i=1,2,ldots,M, n=0,1,ldots,N), denote the deviation between the exact and numerical solutions, and (varepsilon^{n}= varepsilon_{1}^{n}, varepsilon_{2}^{n},ldots, varepsilon_{M}^{n})^{T}).

Figure 2 Comparison between exact solutions and numerical solutions with (pmb{alpha=0.7}), (pmb{h=1/50}), (pmb{tau=0.01}), (pmb{t=0.2}).

The exact and numerical solutions are compared at (t = 0.15).

The comparisons between the analytical solution and the numerical finite difference solution for different ε values when T = 1 are shown in Figures 1 and 2. Figure 1 The exact and numerical solutions of u ( x, 1 ).

The comparisons between the analytical solution and the numerical finite difference solution for ε = 0, 01, ε = 0, 05 values when T = 1 are shown in Figure 1. Figure 1 The exact and numerical solutions of u ( x, 1 ).

Figure 6 shows the exact and the numerical solutions of (r(t)) when (T=1/2). Figure 6 The exact and numerical solutions of  (pmb{r(t)}).

The maximum norm errors between the exact and the numerical solutions are denoted by E_{infty}(h,tau)=max_{1leq nleq N} biglVert u^{n}-U^{n} bigrVert _{infty}.

Good agreement between the exact and the numerical solutions can be observed, even if we have considered (varepsilon = 0.01), and only 10, respectively 15, boundary elements for the boundary discretization.