Compact difference scheme for fourth-order parabolic equation with dispersion
In this paper,a fourth-order compact difference scheme for efficiently solving the fourth-order parabolic equation with dispersion was proposed.The spatial variables of the equation were firstly discretized in the fourth-order compact difference scheme.The system of ordinary differential equations obtained after the discretization was then solved by the cubic Hermite interpolation method and a numerical scheme with fourth-order accuracy in both the spatial and temporal directions was obtained.The Fourier method was used to verify the unconditional stability of the scheme.Numerical experiments was conducted,in which three types of examples were given,and numerical comparisons was made between the proposed scheme and the Crank-Nicolson scheme,which verified the validity of the scheme.Numerical results show that the proposed scheme has good practicability in solving the fourth-order parabolic equations with dispersion.
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