000170073 001__ 170073
000170073 005__ 20260318135945.0
000170073 0247_ $$2doi$$a10.1007/s40314-026-03654-z
000170073 0248_ $$2sideral$$a148625
000170073 037__ $$aART-2026-148625
000170073 041__ $$aeng
000170073 100__ $$aJaiswal, Aishwarya
000170073 245__ $$aA fast robust numerical method for singularly perturbed parabolic convection-diffusion systems with a non-smooth source term
000170073 260__ $$c2026
000170073 5060_ $$aAccess copy available to the general public$$fUnrestricted
000170073 5203_ $$aThis article develops and analyzes a fast robustly convergent numerical method to solve singularly perturbed parabolic convection-diffusion systems, which have a non-smooth source term. The diffusion parameters, which multiply the highest order derivative at each equation of the system, are allowed to be distinct and possibly of varying magnitudes. Then, in general, for sufficiently small values of the diffusion parameters, we observe overlapping boundary layer phenomenon in the exact solution of the continuous problem. Moreover, these boundary layers get accompanied with overlapping interior layers when there is a non-smooth source term in the problem. We establish a priori bounds on the solution and its derivatives, and also a decomposition of the solution into a smooth part, a boundary layer part and an interior layer part. To approximate the solution, we construct a fast numerical method, which uses an upwind finite difference scheme, defined on an appropriate Shishkin type mesh in space and the fractional implicit Euler method combined with the components-wise splitting approach, to discretize in time, on an evenly spaced time grid. This in turn implies that the approximation of the components of the numerical solution become decoupled, permitting us to handle only tridiagonal linear systems of order at each discrete time step. Further, due to overlapping boundary and interior layers the error analysis is challenging and requires the construction of novel barrier functions. It is proven that the proposed numerical method is uniformly convergent with first order accuracy in time and essentially first order in space. Numerical outcomes are presented in the form of tables alongside with a comparison of computational times for various test examples which corroborate in practice the theoretical results. The comparison distinctly illustrates the efficiency of our proposed algorithm.
000170073 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-17R$$9info:eu-repo/grantAgreement/ES/MCINN/PID2022-136441NB-I00
000170073 540__ $$9info:eu-repo/semantics/embargoedAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000170073 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000170073 700__ $$aKumar, Sunil
000170073 700__ $$0(orcid)0000-0003-1263-1996$$aClavero, Carmelo$$uUniversidad de Zaragoza
000170073 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000170073 773__ $$g45, 7 (2026), 267 [41 pp.]$$pComput. Appl. Math.$$tComputational & Applied Mathematics$$x2238-3603
000170073 8564_ $$s3722706$$uhttps://zaguan.unizar.es/record/170073/files/texto_completo.pdf$$yPostprint$$zinfo:eu-repo/date/embargoEnd/2027-03-03
000170073 8564_ $$s2280064$$uhttps://zaguan.unizar.es/record/170073/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint$$zinfo:eu-repo/date/embargoEnd/2027-03-03
000170073 909CO $$ooai:zaguan.unizar.es:170073$$particulos$$pdriver
000170073 951__ $$a2026-03-18-13:58:02
000170073 980__ $$aARTICLE