Uniformly convergent scheme for two‐parameter singularly perturbed problems with non‐smooth data
Devendra Kumar, Parvin Kumari
Abstract
Abstract A numerical scheme is constructed for the problems in which the diffusion and convection parameters ( ϵ 1 and ϵ 2 , respectively) both are small, and the convection and source terms have a jump discontinuity in the domain of consideration. Depending on the magnitude of the ratios , and two different cases have been considered separately. Through rigorous analysis, the theoretical error bounds on the singular and regular components of the solution are obtained separately, which shows that in both cases the method is convergent uniformly irrespective of the size of the parameters ϵ 1 , ϵ 2 . Two test problems are included to validate the theoretical results.
Topics & Concepts
MathematicsDiscontinuity (linguistics)JumpClassification of discontinuitiesMathematical analysisDomain (mathematical analysis)ConvectionApplied mathematicsUniform convergenceConvergence (economics)Convection–diffusion equationMechanicsPhysicsEconomic growthBandwidth (computing)Computer scienceEconomicsComputer networkQuantum mechanicsDifferential Equations and Numerical MethodsMaterial Science and ThermodynamicsAdvanced Mathematical Modeling in Engineering