Based on the radial basis function (RBF) and the singular hybrid boundary node method (SHBNM), this paper presents an inherent meshless, boundary-only technique, which names dual reciprocity singular hybrid boundary node method (DRSHBNM), for numerical solution of various inhomogeneous equations. In this study, the RBFs are employed to approximate the inhomogeneous terms via dual reciprocity method (DRM), while the general solution is solved by means of SHBNM, in which only requires discrete nodes constructed on the boundary of a domain, while several nodes in the domain are needed for the RBF interpolation. The treatment of singularity integration and the 'boundary layer effect' have been given by a series of effective approaches. Numerical examples for the solution of inhomogeneous equations show that high convergence rates and high accuracy with a small node number are achievable.
