{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T03:45:02Z","timestamp":1777866302249,"version":"3.51.4"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1016\/j.matcom.2026.02.033","type":"journal-article","created":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T07:59:40Z","timestamp":1772524780000},"page":"16-33","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A stable and accurate compact exponential scheme for 3D groundwater pollution model: Theory and Comparison"],"prefix":"10.1016","volume":"247","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7929-3069","authenticated-orcid":false,"given":"P.","family":"Roul","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-5510-4919","authenticated-orcid":false,"given":"Vikas","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2026.02.033_b1","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s10712-015-9343-1","article-title":"Modelling freshwater resources at the global scale: challenges and prospects","volume":"37","author":"D\u00f6ll","year":"2016","journal-title":"Surv. Geophys."},{"key":"10.1016\/j.matcom.2026.02.033_b2","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1002\/ird.1658","article-title":"Sustainable groundwater use in agriculture","volume":"61","author":"Madramootoo","year":"2012","journal-title":"Irrig. Drain."},{"key":"10.1016\/j.matcom.2026.02.033_b3","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.apnum.2009.10.008","article-title":"Some reduced finite difference schemes based on a proper orthogonal decomposition technique for parabolic equations","volume":"60","author":"Sun","year":"2010","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.matcom.2026.02.033_b4","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijheatmasstransfer.2019.119179","article-title":"A DFN based 3D numerical approach for modeling coupled groundwater flow and solute transport in fractured rock mass","volume":"149","author":"Li","year":"2020","journal-title":"Int. J. Heat Mass Transfer"},{"issue":"3","key":"10.1016\/j.matcom.2026.02.033_b5","doi-asserted-by":"crossref","first-page":"350","DOI":"10.4236\/ajcm.2017.73025","article-title":"Numerical simulation of groundwater pollution problems based on convection\u2013diffusion equation","volume":"7","author":"Li","year":"2017","journal-title":"Am. J. Comput. Math."},{"key":"10.1016\/j.matcom.2026.02.033_b6","article-title":"Heat transfer and mass transport in the ocean wave-driven free-surface boundary layer","author":"Simone","year":"2025","journal-title":"J. Fluid Mech."},{"key":"10.1016\/j.matcom.2026.02.033_b7","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijthermalsci.2021.106933","article-title":"Meshless finite difference method with B-splines for numerical solution of coupled advection-diffusion-reaction problems","volume":"165","author":"Hidayat","year":"2021","journal-title":"Int. J. Therm. Sci."},{"issue":"6","key":"10.1016\/j.matcom.2026.02.033_b8","doi-asserted-by":"crossref","first-page":"2180","DOI":"10.1108\/HFF-07-2024-0503","article-title":"Computational study on cilia transport of Prandtl nanofluid (blood\u2013Fe_3$O_4$) enhancing convective heat transfer along microorganisms under electroosmotic effects in wavy capillaries","volume":"35","author":"Ajmal","year":"2025","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"issue":"12","key":"10.1016\/j.matcom.2026.02.033_b9","doi-asserted-by":"crossref","first-page":"3278","DOI":"10.1016\/j.cnsns.2013.05.018","article-title":"A new linearized compact multisplitting scheme for the nonlinear convection\u2013reaction\u2013diffusion equations with delay","volume":"18","author":"Zhang","year":"2013","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"10.1016\/j.matcom.2026.02.033_b10","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1016\/j.cam.2018.05.039","article-title":"An energy stable fourth-order finite difference scheme for the Cahn\u2013Hilliard equation","volume":"362","author":"Cheng","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.matcom.2026.02.033_b11","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.enganabound.2018.10.003","article-title":"RBF-based meshless local Petrov Galerkin method for the multi-dimensional convection\u2013diffusion-reaction equation","volume":"98","author":"Li","year":"2019","journal-title":"Eng. Anal. Bound. Elem."},{"key":"10.1016\/j.matcom.2026.02.033_b12","doi-asserted-by":"crossref","DOI":"10.1002\/zamm.201900245","article-title":"An accuracy comparison of piecewise linear reconstruction techniques for the characteristic finite volume method for two-dimensional convection\u2013diffusion equation","volume":"101","author":"Para","year":"2021","journal-title":"Z. Angew. Math. Mech."},{"key":"10.1016\/j.matcom.2026.02.033_b13","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1016\/j.ijheatmasstransfer.2018.01.024","article-title":"Chebyshev spectral element method for natural convection in a porous cavity under local thermal non-equilibrium model","volume":"121","author":"Wang","year":"2018","journal-title":"Int. J. Heat Mass Transfer"},{"issue":"9","key":"10.1016\/j.matcom.2026.02.033_b14","doi-asserted-by":"crossref","first-page":"4281","DOI":"10.1108\/HFF-07-2019-0597","article-title":"A cubic B-spline quasi-interpolation method for solving two-dimensional unsteady advection diffusion equations","volume":"30","author":"Mittal","year":"2020","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"issue":"4","key":"10.1016\/j.matcom.2026.02.033_b15","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1080\/10407790.2013.869095","article-title":"A new high-order compact ADI method for 3-D unsteady convection\u2013diffusion problems with discontinuous coefficients","volume":"65","author":"Zhai","year":"2014","journal-title":"Numer. Heat Transfer B"},{"issue":"1","key":"10.1016\/j.matcom.2026.02.033_b16","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1080\/10407790.2016.1173497","article-title":"New unconditionally stable scheme for solving the convection\u2013diffusion equation based on the Associated Hermite orthogonal functions","volume":"70","author":"Zhang","year":"2016","journal-title":"Numer. Heat Transfer B"},{"key":"10.1016\/j.matcom.2026.02.033_b17","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.cam.2016.04.016","article-title":"The compact and Crank\u2013Nicolson ADI schemes for two-dimensional semilinear multidelay parabolic equations","volume":"306","author":"Zhang","year":"2016","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"10.1016\/j.matcom.2026.02.033_b18","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1023\/A:1021168924020","article-title":"A fourth-order scheme for incompressible Boussinesq equations","volume":"18","author":"Liu","year":"2003","journal-title":"J. Sci. Comput."},{"issue":"3","key":"10.1016\/j.matcom.2026.02.033_b19","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/s00211-003-0508-3","article-title":"Analysis of a fourth-order finite difference method for the incompressible Boussinesq equations","volume":"97","author":"Wang","year":"2004","journal-title":"Numer. Math."},{"key":"10.1016\/j.matcom.2026.02.033_b20","article-title":"Study on groundwater pollution and its human impact analysis using geospatial techniques in semi-urban of south India","volume":"240","author":"Vivek","year":"2024","journal-title":"Environ. Res."},{"key":"10.1016\/j.matcom.2026.02.033_b21","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.jconhyd.2018.11.002","article-title":"A simple contaminant fate and transport modelling tool for management and risk assessment of groundwater pollution from contaminated sites","volume":"221","author":"Locatelli","year":"2019","journal-title":"J. Contam. Hydrol."},{"key":"10.1016\/j.matcom.2026.02.033_b22","doi-asserted-by":"crossref","first-page":"16624","DOI":"10.1038\/s41598-024-67752-w","article-title":"Groundwater contamination modelling in Ayad River Basin","volume":"14","author":"Pareta","year":"2024","journal-title":"Udaipur, Sci. Rep."},{"key":"10.1016\/j.matcom.2026.02.033_b23","doi-asserted-by":"crossref","DOI":"10.1016\/j.jenvman.2021.113161","article-title":"A comprehensive review of groundwater vulnerability assessment using index-based, modelling, and coupling methods","volume":"296","author":"Goyal","year":"2021","journal-title":"J. Env. Manag."},{"key":"10.1016\/j.matcom.2026.02.033_b24","series-title":"Groundwater Pollution","author":"Fried","year":"1975"},{"issue":"1","key":"10.1016\/j.matcom.2026.02.033_b25","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.ifacol.2015.05.149","article-title":"Alternative approaches for groundwater pollution","volume":"48","author":"Winkler","year":"2015","journal-title":"IFAC-PapersOnLine"},{"issue":"6","key":"10.1016\/j.matcom.2026.02.033_b26","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1029\/WR019i006p01489","article-title":"A proposed upstream weight numerical method for simulating pollutant transport in groundwater","volume":"19","author":"Sun","year":"1983","journal-title":"Water Resour. Res."},{"issue":"1\u20132","key":"10.1016\/j.matcom.2026.02.033_b27","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.mcm.2007.02.006","article-title":"Flux-limiting techniques for simulation of pollutant transport in porous media: Application to groundwater management","volume":"47","author":"Smaoui","year":"2008","journal-title":"Math. Comput. Modelling"},{"issue":"1","key":"10.1016\/j.matcom.2026.02.033_b28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/num.1690110103","article-title":"Optimal-order convergence rates for Eulerian\u2013Lagrangian localized adjoint methods for reactive transport and contamination in groundwater","volume":"11","author":"Wang","year":"1995","journal-title":"Numer. Methods Partial. Differ. Equ."},{"key":"10.1016\/j.matcom.2026.02.033_b29","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1186\/s13662-018-1652-5","article-title":"Fourth-order compact finite difference method for solving two-dimensional convection\u2013diffusion equation","volume":"2018","author":"Li","year":"2018","journal-title":"Adv. Differ. Equ."},{"issue":"1","key":"10.1016\/j.matcom.2026.02.033_b30","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.cam.2005.12.005","article-title":"A fourth-order compact ADI method for solving two-dimensional unsteady convection\u2013diffusion problems","volume":"198","author":"Tian","year":"2007","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"10.1016\/j.matcom.2026.02.033_b31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcp.2004.01.002","article-title":"High order ADI method for solving unsteady convection\u2013diffusion problems","volume":"198","author":"Karaa","year":"2004","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.matcom.2026.02.033_b32","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1016\/j.cam.2013.06.001","article-title":"A high-order compact exponential scheme for the fractional convection\u2013diffusion equation","volume":"255","author":"Cui","year":"2014","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"10.1016\/j.matcom.2026.02.033_b33","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1007\/s10915-012-9621-8","article-title":"Stability and convergence analysis of a fully discrete Fourier collocation spectral method for the three-dimensional viscous Burgers\u2019 equation","volume":"53","author":"Gottlieb","year":"2012","journal-title":"J. Sci. Comput."},{"issue":"4","key":"10.1016\/j.matcom.2026.02.033_b34","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1093\/imanum\/drv065","article-title":"Stability and convergence of a second-order mixed finite element method for the Cahn\u2013Hilliard equation","volume":"36","author":"Diegel","year":"2016","journal-title":"IMA J. Numer. Anal."},{"issue":"5","key":"10.1016\/j.matcom.2026.02.033_b35","doi-asserted-by":"crossref","first-page":"3123","DOI":"10.1137\/16M1061588","article-title":"Long-time stability of high-order multistep numerical schemes for two-dimensional incompressible Navier\u2013Stokes equations","volume":"54","author":"Cheng","year":"2016","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426000807?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426000807?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T08:24:28Z","timestamp":1777537468000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475426000807"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":35,"alternative-id":["S0378475426000807"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2026.02.033","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A stable and accurate compact exponential scheme for 3D groundwater pollution model: Theory and Comparison","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2026.02.033","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}]}}