Gracia, J. L.; O’Riordan, E. A singularly perturbed convection-diffusion parabolic problem with incompatible boundary/initial data. (English) Zbl 07710412 Appl. Numer. Math. 190, 168-186 (2023). MSC: 65Mxx 65Nxx 35Bxx PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{E. O'Riordan}, Appl. Numer. Math. 190, 168--186 (2023; Zbl 07710412) Full Text: DOI arXiv
Gracia, J. L.; O’Riordan, E. Singularly perturbed reaction-diffusion problems with discontinuities in the initial and/or the boundary data. (English) Zbl 1432.35011 J. Comput. Appl. Math. 370, Article ID 112638, 17 p. (2020). MSC: 35B25 35K20 35K57 65M06 65M12 65M15 65M70 35R05 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{E. O'Riordan}, J. Comput. Appl. Math. 370, Article ID 112638, 17 p. (2020; Zbl 1432.35011) Full Text: DOI arXiv
Clavero, C.; Gracia, J. L. Uniformly convergent additive schemes for 2D singularly perturbed parabolic systems of reaction-diffusion type. (English) Zbl 1412.65069 Numer. Algorithms 80, No. 4, 1097-1120 (2019). MSC: 65M06 65N06 35K67 65N55 35K57 65M12 65N12 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, Numer. Algorithms 80, No. 4, 1097--1120 (2019; Zbl 1412.65069) Full Text: DOI Link
Clavero, Carmelo; Gracia, José Luis Efficient numerical methods for singularly perturbed systems of reaction-diffusion type. (English) Zbl 1448.65098 López de Silanes, M. C. (ed.) et al., Fourteenth international conference Zaragoza-Pau on mathematics and its applications. Proceedings of the conference, Jaca, Spain, September 12–15, 2016. Zaragoza: Prensas de la Universidad de Zaragoza. Monogr. Mat. García Galdeano 41, 63-74 (2018). MSC: 65M06 65N06 65M12 35K57 35B25 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, Monogr. Mat. García Galdeano 41, 63--74 (2018; Zbl 1448.65098)
Gracia, José Luis; O’Riordan, Eugene; Stynes, Martin Convergence in positive time for a finite difference method applied to a fractional convection-diffusion problem. (English) Zbl 1382.65275 Comput. Methods Appl. Math. 18, No. 1, 33-42 (2018). MSC: 65M12 35K20 35R11 65M06 65M15 PDFBibTeX XMLCite \textit{J. L. Gracia} et al., Comput. Methods Appl. Math. 18, No. 1, 33--42 (2018; Zbl 1382.65275) Full Text: DOI
Clavero, C.; Gracia, J. L.; Shishkin, G. I.; Shishkina, L. P. An efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers. (English) Zbl 1357.65115 J. Comput. Appl. Math. 318, 634-645 (2017). MSC: 65M06 35K57 35B25 65M50 65M12 PDFBibTeX XMLCite \textit{C. Clavero} et al., J. Comput. Appl. Math. 318, 634--645 (2017; Zbl 1357.65115) Full Text: DOI
Stynes, Martin; Gracia, José Luis Blow-up of solutions and interior layers in a Caputo two-point boundary value problem. (English) Zbl 1427.65123 Knobloch, Petr (ed.), Boundary and interior layers, computational and asymptotic methods – BAIL 2014. Proceedings of the conference, Prague, Czech Republic, September 15–19, 2014. Cham: Springer. Lect. Notes Comput. Sci. Eng. 108, 293-302 (2015). MSC: 65L10 34A08 PDFBibTeX XMLCite \textit{M. Stynes} and \textit{J. L. Gracia}, Lect. Notes Comput. Sci. Eng. 108, 293--302 (2015; Zbl 1427.65123) Full Text: DOI
Gracia, José Luis; Stynes, Martin Boundary layers in a Riemann-Liouville fractional derivative two-point boundary value problem. (English) Zbl 1427.65119 Knobloch, Petr (ed.), Boundary and interior layers, computational and asymptotic methods – BAIL 2014. Proceedings of the conference, Prague, Czech Republic, September 15–19, 2014. Cham: Springer. Lect. Notes Comput. Sci. Eng. 108, 87-98 (2015). MSC: 65L10 34A08 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{M. Stynes}, Lect. Notes Comput. Sci. Eng. 108, 87--98 (2015; Zbl 1427.65119) Full Text: DOI
Gracia, J. L.; O’Riordan, E. Scaled discrete derivatives of singularly perturbed elliptic problems. (English) Zbl 1312.65171 Numer. Methods Partial Differ. Equations 31, No. 1, 225-252 (2015). Reviewer: Srinivasan Natesan (Assam) MSC: 65N06 35B25 35J25 65N12 65N15 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{E. O'Riordan}, Numer. Methods Partial Differ. Equations 31, No. 1, 225--252 (2015; Zbl 1312.65171) Full Text: DOI
Gracia, J. L.; O’Riordan, E. Numerical approximation of solution derivatives in the case of singularly perturbed time dependent reaction-diffusion problems. (English) Zbl 1295.65085 J. Comput. Appl. Math. 273, 13-24 (2015). MSC: 65M06 35K57 35B25 65M50 65M12 65M15 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{E. O'Riordan}, J. Comput. Appl. Math. 273, 13--24 (2015; Zbl 1295.65085) Full Text: DOI
Gracia, José Luis On the uniform convergence of singularly perturbed reaction-diffusion problems with non-smooth data. (English) Zbl 1360.65210 López de Silanes, M. C. (ed.) et al., Twelfth international conference Zaragoza-Pau on mathematics. Proceedings of the conference, Jaca, Spain, September 17–19, 2012. Zaragoza: Prensas de la Universidad de Zaragoza (ISBN 978-84-16028-35-1/pbk). Monografías Matemáticas “García de Galdeano” 39, 121-131 (2014). MSC: 65M06 65M12 65M50 35K57 PDFBibTeX XMLCite \textit{J. L. Gracia}, Monogr. Mat. García Galdeano 39, 121--131 (2014; Zbl 1360.65210)
Clavero, C.; Gracia, J. L. Uniformly convergent additive finite difference schemes for singularly perturbed parabolic reaction-diffusion systems. (English) Zbl 1350.65086 Comput. Math. Appl. 67, No. 3, 655-670 (2014). MSC: 65M06 35K57 35B25 65M50 65M12 65M20 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, Comput. Math. Appl. 67, No. 3, 655--670 (2014; Zbl 1350.65086) Full Text: DOI
Clavero, C.; Gracia, J. L. An improved uniformly convergent scheme in space for 1D parabolic reaction-diffusion systems. (English) Zbl 1336.65132 Appl. Math. Comput. 243, 57-73 (2014). MSC: 65M06 65M12 65M50 35K57 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, Appl. Math. Comput. 243, 57--73 (2014; Zbl 1336.65132) Full Text: DOI
Shishkin, Grigory; Shishkina, Lidia; Gracia, Jose Luis; Clavero, Carmelo On a numerical technique to study difference schemes for singularly perturbed parabolic reaction-diffusion equations. (English) Zbl 1315.65075 Int. J. Numer. Anal. Model. 11, No. 2, 412-426 (2014). MSC: 65M06 35B25 35K57 65M15 PDFBibTeX XMLCite \textit{G. Shishkin} et al., Int. J. Numer. Anal. Model. 11, No. 2, 412--426 (2014; Zbl 1315.65075) Full Text: Link
Clavero, C.; Gracia, J. L.; Shishkin, G. I.; Shishkina, L. P. Grid approximation of a singularly perturbed parabolic equation with degenerating convective term and discontinuous right-hand side. (English) Zbl 1279.65098 Int. J. Numer. Anal. Model. 10, No. 4, 795-814 (2013). MSC: 65M06 35K20 35R05 35K65 65M12 65M15 35B25 PDFBibTeX XMLCite \textit{C. Clavero} et al., Int. J. Numer. Anal. Model. 10, No. 4, 795--814 (2013; Zbl 1279.65098) Full Text: Link
Gracia, J. L.; O’Riordan, E. A singularly perturbed reaction-diffusion problem with incompatible boundary-initial data. (English) Zbl 1352.65237 Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 5th international conference, NAA 2012, Lozenetz, Bulgaria, June 15–20, 2012. Revised selected papers. Berlin: Springer (ISBN 978-3-642-41514-2/pbk). Lecture Notes in Computer Science 8236, 303-310 (2013). MSC: 65M06 35K57 65M50 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{E. O'Riordan}, Lect. Notes Comput. Sci. 8236, 303--310 (2013; Zbl 1352.65237) Full Text: DOI
Gracia, J. L.; O’Riordan, E. A singularly perturbed parabolic problem with a layer in the initial condition. (English) Zbl 1302.65189 Appl. Math. Comput. 219, No. 2, 498-510 (2012). MSC: 65M06 65M12 35K57 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{E. O'Riordan}, Appl. Math. Comput. 219, No. 2, 498--510 (2012; Zbl 1302.65189) Full Text: DOI
Gracia, J. L.; O’Riordan, E. A singularily perturbed convection-diffusion problem with a moving interior layer. (English) Zbl 1270.65047 Int. J. Numer. Anal. Model. 9, No. 4, 823-843 (2012). Reviewer: Srinivasan Natesan (Assam) MSC: 65M06 35B25 35K20 65M12 65M15 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{E. O'Riordan}, Int. J. Numer. Anal. Model. 9, No. 4, 823--843 (2012; Zbl 1270.65047) Full Text: Link
Clavero, C.; Gracia, J. L. A high order HODIE finite difference scheme for 1D parabolic singularly perturbed reaction-diffusion problems. (English) Zbl 1245.65108 Appl. Math. Comput. 218, No. 9, 5067-5080 (2012). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65M12 35K57 35B25 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, Appl. Math. Comput. 218, No. 9, 5067--5080 (2012; Zbl 1245.65108) Full Text: DOI
Clavero, C.; Gracia, J. L.; Stynes, M. A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems. (English) Zbl 1225.65084 J. Comput. Appl. Math. 235, No. 17, 5240-5248 (2011). Reviewer: K. N. Shukla (Gurgaon) MSC: 65M06 35K20 65M12 PDFBibTeX XMLCite \textit{C. Clavero} et al., J. Comput. Appl. Math. 235, No. 17, 5240--5248 (2011; Zbl 1225.65084) Full Text: DOI
Clavero, Carmelo; Gracia, José Luis; Lisbona, Fransisco Second order uniform approximations for the solution of time dependent singularly perturbed reaction-diffusion systems. (English) Zbl 1214.65044 Int. J. Numer. Anal. Model. 7, No. 3, 428-443 (2010). Reviewer: S. Burys (Kraków) MSC: 65M06 65M12 65M20 35K20 35B25 PDFBibTeX XMLCite \textit{C. Clavero} et al., Int. J. Numer. Anal. Model. 7, No. 3, 428--443 (2010; Zbl 1214.65044) Full Text: Link
Clavero, C.; Gracia, J. L.; Lisbona, F. J. An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems. (English) Zbl 1195.65101 J. Comput. Appl. Math. 234, No. 8, 2501-2515 (2010). Reviewer: R. Militaru (Craiova) MSC: 65L12 65L10 34B05 34E15 65L50 65L70 PDFBibTeX XMLCite \textit{C. Clavero} et al., J. Comput. Appl. Math. 234, No. 8, 2501--2515 (2010; Zbl 1195.65101) Full Text: DOI
Clavero, C.; Gracia, J. L. On the uniform convergence of a finite difference scheme for time dependent singularly perturbed reaction-diffusion problems. (English) Zbl 1192.65118 Appl. Math. Comput. 216, No. 5, 1478-1488 (2010). Reviewer: Vit Dolejsi (Praha) MSC: 65M12 65M06 65M20 65M50 35B25 35K57 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, Appl. Math. Comput. 216, No. 5, 1478--1488 (2010; Zbl 1192.65118) Full Text: DOI
Gracia, J. L.; Lisbona, F. J.; O’Riordan, E. A coupled system of singularly perturbed parabolic reaction-diffusion equations. (English) Zbl 1188.65118 Adv. Comput. Math. 32, No. 1, 43-61 (2010). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M06 65M15 65M12 65M50 35K57 35B25 PDFBibTeX XMLCite \textit{J. L. Gracia} et al., Adv. Comput. Math. 32, No. 1, 43--61 (2010; Zbl 1188.65118) Full Text: DOI
Gracia, J. L.; Lisbona, F. J.; Madaune-Tort, M.; O’Riordan, E. A system of singularly perturbed semilinear equations. (English) Zbl 1180.65090 Hegarty, Alan F. (ed.) et al., BAIL 2008 – Boundary and interior layers. Proceedings of the international conference on boundary and interior layers – computational and asymptotic methods, Limerick, Ireland, July 28–August 1, 2008. Berlin: Springer (ISBN 978-3-642-00604-3/pbk; 978-3-642-00605-0/ebook). Lecture Notes in Computational Science and Engineering 69, 163-172 (2009). MSC: 65L10 34B15 34E15 65L50 65L20 PDFBibTeX XMLCite \textit{J. L. Gracia} et al., Lect. Notes Comput. Sci. Eng. 69, 163--172 (2009; Zbl 1180.65090) Full Text: DOI
Clavero, C.; Gracia, J. L.; Lisbona, F. J. High order schemes for reaction-diffusion singularly perturbed systems. (English) Zbl 1181.65104 Hegarty, Alan F. (ed.) et al., BAIL 2008 – Boundary and interior layers. Proceedings of the international conference on boundary and interior layers – computational and asymptotic methods, Limerick, Ireland, July 28–August 1, 2008. Berlin: Springer (ISBN 978-3-642-00604-3/pbk; 978-3-642-00605-0/ebook). Lecture Notes in Computational Science and Engineering 69, 107-115 (2009). MSC: 65L10 34B05 34E15 65L12 65L70 65L50 PDFBibTeX XMLCite \textit{C. Clavero} et al., Lect. Notes Comput. Sci. Eng. 69, 107--115 (2009; Zbl 1181.65104) Full Text: DOI Link
Bujanda, B.; Clavero, C.; Gracia, J. L.; Jorge, J. C. A high order uniformly convergent alternating direction scheme for time dependent reaction-diffusion singularly perturbed problems. (English) Zbl 1125.65079 Numer. Math. 107, No. 1, 1-25 (2007). Reviewer: Othmar Koch (Baden) MSC: 65M06 35B25 35K57 65M12 PDFBibTeX XMLCite \textit{B. Bujanda} et al., Numer. Math. 107, No. 1, 1--25 (2007; Zbl 1125.65079) Full Text: DOI
Gracia, J. L.; Lisbona, F. J. A uniformly convergent scheme for a system of reaction-diffusion equations. (English) Zbl 1119.65079 J. Comput. Appl. Math. 206, No. 1, 1-16 (2007). Reviewer: Othmar Koch (Baden) MSC: 65M06 65M12 35K57 35B25 65M50 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{F. J. Lisbona}, J. Comput. Appl. Math. 206, No. 1, 1--16 (2007; Zbl 1119.65079) Full Text: DOI
Gracia, J. L.; O’Riordan, E. A defect-correction parameter-uniform numerical method for a singularly perturbed convection-diffusion problem in one dimension. (English) Zbl 1098.65083 Numer. Algorithms 41, No. 4, 359-385 (2006). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65L10 65L70 65L12 34B05 34E15 65L20 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{E. O'Riordan}, Numer. Algorithms 41, No. 4, 359--385 (2006; Zbl 1098.65083) Full Text: DOI
Gracia, J. L.; Clavero, C. A compact finite difference scheme for 2D reaction-diffusion singularly perturbed problems. (English) Zbl 1092.65090 J. Comput. Appl. Math. 192, No. 1, 152-167 (2006). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 65N06 35J25 35B25 65N12 PDFBibTeX XMLCite \textit{J. L. Gracia} and \textit{C. Clavero}, J. Comput. Appl. Math. 192, No. 1, 152--167 (2006; Zbl 1092.65090) Full Text: DOI
Clavero, C.; Gracia, J. L. High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems. (English) Zbl 1080.65062 Appl. Math. Comput. 168, No. 2, 1109-1127 (2005). Reviewer: Emil Minchev (Tokyo) MSC: 65L10 65L06 34B05 34E15 65L20 35B25 65M20 35K15 65M50 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, Appl. Math. Comput. 168, No. 2, 1109--1127 (2005; Zbl 1080.65062) Full Text: DOI
Clavero, C.; Gracia, J. L.; O’Riordan, E. A parameter robust numerical method for a two dimensional reaction-diffusion problem. (English) Zbl 1086.65101 Math. Comput. 74, No. 252, 1743-1758 (2005). Reviewer: Georg Hebermehl (Berlin) MSC: 65N06 65N12 65N15 35J25 PDFBibTeX XMLCite \textit{C. Clavero} et al., Math. Comput. 74, No. 252, 1743--1758 (2005; Zbl 1086.65101) Full Text: DOI
Clavero, C.; Gracia, J. L.; Jorge, J. C. High-order numerical methods for one-dimensional parabolic singularly perturbed problems with regular layers. (English) Zbl 1073.65079 Numer. Methods Partial Differ. Equations 21, No. 1, 149-169 (2005). Reviewer: Snezhana Gocheva-Ilieva (Plovdiv) MSC: 65M06 35K15 35B25 65M50 65M12 PDFBibTeX XMLCite \textit{C. Clavero} et al., Numer. Methods Partial Differ. Equations 21, No. 1, 149--169 (2005; Zbl 1073.65079) Full Text: DOI
Clavero, C.; Gracia, J. L. HODIE finite difference schemes on generalized Shishkin meshes. (English) Zbl 1046.65064 J. Comput. Appl. Math. 164-165, 195-206 (2004). Reviewer: J. D. P. Donnelly (Oxford) MSC: 65L12 65L10 34B05 65L50 34E15 65L20 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, J. Comput. Appl. Math. 164--165, 195--206 (2004; Zbl 1046.65064) Full Text: DOI
Gracia, J. L.; Jorge, J. C.; Bujanda, B.; Clavero, C. High order uniformly convergent fractional step RK methods and HODIE finite difference schemes for 2D evolutionary convection-diffusion problems. (English) Zbl 1049.65096 J. Comput. Methods Sci. Eng. 3, No. 3, 403-413 (2003). MSC: 65M20 35K15 35B25 65M06 65L06 65M50 65M12 PDFBibTeX XMLCite \textit{J. L. Gracia} et al., J. Comput. Methods Sci. Eng. 3, No. 3, 403--413 (2003; Zbl 1049.65096)
Clavero, C.; Gracia, J. L. A HODIE method for 2D parabolic problems of convection-diffusion type. (English) Zbl 1041.65068 Madaune-Tort, M. (ed.) et al., 7th Zaragoza-Pau conference on applied and statistical mathematics, Jaca (Huesca), September 17–18, 2001. Zaragoza: Univ. de Zaragoza, Seminario Matemático “García de Galdeano” (ISBN 84-96214-04-4/pbk). Monogr. Semin. Mat. “García de Galdeano” 27, 217-224 (2003). MSC: 65M06 65M12 35K15 65M50 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, in: VII Journadas Zaragoza-Pau de Matemática aplicada y Estadística, Jaca (Huesca), 17--18 de septiembre de 2001. Zaragoza: Univ. de Zaragoza, Seminario Matemático ``García de Galdeano''. 217--224 (2003; Zbl 1041.65068)
Clavero, C.; Gracia, J. L.; Lisbona, F.; Shishkin, G. I. A robust method of improved order for convection-diffusion problems in a domain with characteristic boundaries. (English) Zbl 1012.65104 ZAMM, Z. Angew. Math. Mech. 82, No. 9, 631-647 (2002). Reviewer: Leonid B.Chubarov (Novosibirsk) MSC: 65N06 76M20 35J25 35B25 65N12 65N50 PDFBibTeX XMLCite \textit{C. Clavero} et al., ZAMM, Z. Angew. Math. Mech. 82, No. 9, 631--647 (2002; Zbl 1012.65104) Full Text: DOI
Gracia, J. L.; Clavero, C.; Lisbona, F. Numerical approximation of convection-diffusion problems using an improved upwind scheme on a Shishkin mesh. (Spanish) Zbl 0993.65116 Cruz Lopez de Silanes, Maria (ed.) et al., Actes des 6èmes journées Zaragoza-Pau de mathématiques appliquées et de statistiques. Pau: Publications de Université de Pau et Pays de l’Adour, PUP. 289-296 (2001). MSC: 65N06 35B25 65N12 35J25 65N50 PDFBibTeX XMLCite \textit{J. L. Gracia} et al., in: Actes des 6èmes journées Zaragoza-Pau de mathématiques appliquées et de statistiques. Pau: Publications de Université de Pau et Pays de l'Adour, PUP. 289--296 (2001; Zbl 0993.65116)
Gracia, J. L.; Lisbona, F.; Clavero, C. High order \(\varepsilon\)-uniform methods for singularly perturbed reaction-diffusion problems. (English) Zbl 0978.65066 Vulkov, Lubin (ed.) et al., Numerical analysis and its applications. 2nd international conference, NAA 2000, Rousse, Bulgaria, June 11-15, 2000. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 1988, 350-358 (2001). MSC: 65L10 65L12 65L20 65L50 34B05 34E15 PDFBibTeX XMLCite \textit{J. L. Gracia} et al., Lect. Notes Comput. Sci. 1988, 350--358 (2001; Zbl 0978.65066)
Clavero, C.; Gracia, J. L. Uniform convergence of a classical scheme on Shishkin meshes for a convection-diffusion problem. (Spanish. English summary) Zbl 0934.65080 Proceedings of the 15th congress on differential equations and applications and congress on applied mathematics, Vigo, Spain, September 23-26, 1997. Vols. I and II. Vigo: Servicio de Publicacións da Universidade de Vigo. Colecc. Congr. 9, 237-242 (1998). MSC: 65L10 34B05 34E15 65L12 65L20 65L50 PDFBibTeX XMLCite \textit{C. Clavero} and \textit{J. L. Gracia}, in: XV Congreso de ecuaciones diferenciales y aplicaciones y congreso de matemática aplicada, Vigo, España, 23--26 Septiembre 1997. Volumen I e II. Vigo: Servicio de Publicacións da Universidade de Vigo. 237--242 (1998; Zbl 0934.65080)