A boundary-only treatment by singular boundary method for two-dimensional inhomogeneous problems

•A boundary-only singular boundary method is proposed for inhomogeneous problems.•The method unifies the MRM and SBM.•The boundary-only merit decreases the quantity of preparing data.•The simple formulas of the origin intensity factors are derived for high-order fundamental solutions.•The MRM–SBM performs well in problems with corner singularities.