High-Order Compact Difference Methods and Their Convergence for Semi-Linear Delay Sobolev Equations
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Delay Sobolev equations (DSEs), a kind of pseudo-parabolic equation with delay, are widely used in diffusion or transport with memory, flow in the fluid and other related fields. In this paper, two high-order compact difference methods (HOCD-I and HOCD-II) are introduced to solve the semi-linear DSEs. Moreover, the convergence of the methods are proved. Finally, in order to testify the accuracy and the convergence rate of the methods, two concrete numerical experiments are presented.