2022/08/08 by Nirmali Roy, Roy, Nirmali, Anuradha Jha +1
Engineering · Mathematics · #65L10 #65L11 #65L20 #65L70 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2208.04375
openalex publication_date 2022/08/08 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
A two-parameter singularly perturbed problem with discontinuous source and convection coefficient is considered in one dimension. Both convection coefficient and source term are discontinuous at a point in the domain. The presence of perturbation parameters results in boundary layers at the boundaries. Also, an interior layer occurs due to the discontinuity of data at an interior point. An upwind scheme on an appropriately defined Shishkin-Bakhvalov mesh is used to resolve the boundary layers and interior layers. A three-point formula is used at the point of discontinuity. The proposed method has first-order parameter uniform convergence. Theoretical error estimates derived are verified using the numerical method on some test problems. Numerical results authenticate the claims made. The use of the Shiskin-Bakhvalov mesh helps achieve the first-order convergence, unlike the Shishkin mesh, where the order of convergence deteriorates due to a logarithmic term.