A fast accurate artificial boundary condition for the Euler-Bernoulli beam

It is difficult to convert the PDEs defined on the whole space with higher order space derivatives into initial boundary value problems by proposing boundary conditions. In this paper, we use an absorbing boundary condition method to solve the Cauchy problem for one-dimensional Euler-Bernoulli beam with fast convolution boundary condition which is derived through the Padé approximation for the square root function √(·) . We also introduce a constant damping term to control the error between the resulting approximation of the Euler-Bernoulli system and the original one. Numerical examples verify the theoretical results and demonstrate the performance for the fast numerical method.