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Keywords:
regularized long wave equation; integral method with variational limit; finite difference method; Lagrange interpolation; energy conservation scheme
regularized long wave equation; integral method with variational limit; finite difference method; Lagrange interpolation; energy conservation scheme
Summary:
An energy conservative scheme is proposed for the regularized long wave (RLW) equation. The integral method with variational limit is used to discretize the spatial derivative and the finite difference method is used to discretize the time derivative. The energy conservation of the scheme and existence of the numerical solution are proved. The convergence of the order $O(h^2 + \tau ^2)$ and unconditional stability are also derived. Numerical examples are carried out to verify the correctness of the theoretical analysis.
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