<p>This paper aims to present a new method based on spline-in-tension approximations for the solution of a class of two-point Robin boundary value problems. The exponential spline function compactly approximates the differential equations at off-step points and one central point, and Robin boundary conditions at two points near the boundary with third-order accuracy. With Dirichlet boundary conditions, the proposed method is directly applicable to solve singular problems. The proposed compact spline method is designed on the variable mesh to capture the rapid change by adjusting the mesh concentration to solve the singular perturbation problems. The error analysis of the suggested method is described using the tridiagonal matrix analysis approach to prove that the coefficient matrix is irreducible and monotone, and the third-order convergence of the proposed method. Numerous application-based linear and non-linear perturbation problems with Robin boundary conditions are solved and compared with the existing methods.</p>