Sentence examples for by present method at from inspiring English sources
Solution of generalize Burger Fisher equation for (a=0.001, b=0.001 text {and} gamma = 1) by present method at (M=M'=5, k=k'=4 text {and} r=4) is given in Table 1.
Open image in new window Fig. 1 Comparison of the numerical results by present method at (r=4) and different values of (k,k',M,M') with exact solution of generalized Burger Fisher equation.
The real and imaginary parts of the absolute errors obtained by the present method at (N=M=20), (alpha _{1}=beta _{1}=alpha _{2}=betare{2}=0) are shown in Figures 1 and 2, respectively.
The absolute differences between the values of the conservative constants obtained by the present method at times t=0 and t=1 are Δ I 1 =4.8×10 −2, Δ I 2 =9.5×10 −3,Δ I 3 =4.1×10 −2. Figure 3 shows the interaction of these solitary waves at different times.
In fact, the approximate solutions obtained by the present method at 1 < ν ≤ 2, 0 < μ ≤ 1 with N = 14 are shown in Figure 4 and Figure 5 to make it easier to show that; as ν and μ approach to their integer values, the solution of fractional order Langevin equation approaches to the solution of integer order Langevin differential equation.
The absolute difference between the values of the conservative constants obtained by the present method at times t = 0 and t = 45 are Δ I 1 = 2.6 × 10 − 1, Δ I 2 = 3.4 × 10 − 1, Δ I 3 = 3.4 × 10 − 3, respectively.
For the (−45/45)s case, however, it is found that a nearly converged solution (less than 5% convergence by doubling the mesh) by the present method is at significant variance with the previous ones that are lack-of-convergence checks.
Synthetic data, representing the random vibrations of systems with hysteresis, validate the estimated system parameters by the presented identification method at low and high-levels of excitation amplitudes.
The present method is antediluvian.
By cubic spline method, at different time points, equation (8) can be presented as the following equation.
