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In this article, we devote ourselves to establishing a natural boundary element (NBE) method for the Sobolev equation in the 2D unbounded domain. To this end, we first constitute the time semi-discretized super-convergence format for the Sobolev equation by means of the Newmark method. Then, using the principle of natural boundary reduction, we establish a fully discretized NBE format based on the natural integral equation and the Poisson integral formula of this problem and analyze the errors between the exact solution and the fully discretized NBE solutions. Finally, we use some numerical experiments to verify that the NBE method is effective and feasible for solving the Sobolev equation in the 2D unbounded domain.

A natural boundary element method for the Sobolev equation in the 2D unbounded domain