The stability and convergence analysis for singularly perturbed Sobolev problems with Robin type boundary condition

This paper presents the robust and stable difference scheme to estimate singularly perturbed Sobolev boundary value problems with Robin type boundary condition. Firstly, the asymptotic behavior of the solution is analyzed. By using interpolating quadrature rules and basis functions, a completely exponentially fitted tree-level difference scheme is constructed on the uniform mesh. Then an error estimation is investigated in a discrete energy norm. Two numerical examples are solved and the computational results are tabulated.