Novel WENO-format high-precision fractional derivative approximation method
A fractional derivative, high-precision technology, applied in electrical digital data processing, complex mathematical operations, CAD numerical modeling, etc., can solve problems such as complex and cumbersome calculation processes
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Embodiment 1
[0125] Embodiment 1: The following fractional differential equation is given
[0126]
[0127] The initial conditions are:
[0128]
[0129] The boundary conditions are:
[0130] u(-L,t)=1, u(L,t)=0; (19)
[0131] in V=0.5 and L=1 or 10.
[0132] exist Figure 1-12 In the numerical simulation of , take D=0.02, L=1, h=2 / N, grid points N=100, time step τ=0.4h 2 , Figure 1-4 , Figure 5-8 , Figure 9-12 Numerical solutions of fractional derivatives of different orders α=1.2, 1.4, 1.6, 1.8 at T=0.001 are given respectively, and it can be noticed that the sharp transition is preserved for different α numerical simulations.
[0133] exist Figure 13-15 In the numerical simulation of , take D=0.2, L=10, h=20 / N, grid points N=200, time step τ=0.4h 2 , Figure 13-15 Numerical solutions of fractional derivative α=1.8 at T=1,2,3 are given.
[0134] exist Figure 16-18 In the numerical simulation of , take D=0.2, L=10, h=20 / N, grid points N=200, time step τ=0.3h 1.8 ...
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