Singularly perturbed robin type boundary value problems with discontinuous source term in geophysical fluid dynamics

Singularly perturbed robin type boundary value problems with discontinuous source terms applicable in geophysical fluid are considered. Due to the discontinuity, interior layers appear in the solution. To fit the interior and boundary layers, a fitted nonstandard numerical method is constructed. To treat the robin boundary condition, we use a finite difference formula. The stability and parameter uniform convergence of the proposed method is proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter, ε, and mesh size, h. The numerical result is tabulated, and it is observed that the present method is more accurate and uniformly convergent with order of convergence of O(h).