Abstract: In this paper, the complete multiple reciprocity method is adopted to solve the one-dimensional (1D) Helmholtz equation for the semiin®nite
domain. In order to recover the information that is missing when the conventional multiple reciprocity method is used, an appropriate
complex number in the zeroth order fundamental solution is added such that the kernels derived using this proposed method are fully
equivalent to those derived using the complex-valued formulation. Two examples including the Dirichlet and Neumann boundary conditions
are investigated to show the validity of the proposed method analytically and numerically. The numerical results show good agreement with
the analytical solutions. q 2001 Elsevier Science Ltd. All rights reserved.