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

Abstract It is difficult to propose boundary conditions for the PDEs with higher order space derivatives like Euler-Bernoulli beam. In this paper we use a 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 Euler-Bernoulli system and the original one. Numerical examples verify the theoretical results and demonstrate the performance for the fast numerical method.