Qiu, Yuchi; Chen, Weitao; Nie, Qing A hybrid method for stiff reaction-diffusion equations. (English) Zbl 1426.65130 Discrete Contin. Dyn. Syst., Ser. B 24, No. 12, 6387-6417 (2019). MSC: 65M06 35K57 65M12 65M15 PDFBibTeX XMLCite \textit{Y. Qiu} et al., Discrete Contin. Dyn. Syst., Ser. B 24, No. 12, 6387--6417 (2019; Zbl 1426.65130) Full Text: DOI
Lei, Jinzhi; Lo, Wing-Cheong; Nie, Qing Mathematical models of morphogen dynamics and growth control. (English) Zbl 1378.35168 Ann. Math. Sci. Appl. 1, No. 2, 427-471 (2016). MSC: 35K57 92C15 35Q92 92B05 PDFBibTeX XMLCite \textit{J. Lei} et al., Ann. Math. Sci. Appl. 1, No. 2, 427--471 (2016; Zbl 1378.35168) Full Text: DOI
Ta, Catherine; Wang, Dongyong; Nie, Qing An integration factor method for stochastic and stiff reaction-diffusion systems. (English) Zbl 1349.65540 J. Comput. Phys. 295, 505-522 (2015). MSC: 65M75 35K57 35R60 PDFBibTeX XMLCite \textit{C. Ta} et al., J. Comput. Phys. 295, 505--522 (2015; Zbl 1349.65540) Full Text: DOI
Wang, Dongyong; Chen, Weitao; Nie, Qing Semi-implicit integration factor methods on sparse grids for high-dimensional systems. (English) Zbl 1349.65340 J. Comput. Phys. 292, 43-55 (2015). MSC: 65M06 65M22 35K57 PDFBibTeX XMLCite \textit{D. Wang} et al., J. Comput. Phys. 292, 43--55 (2015; Zbl 1349.65340) Full Text: DOI Link
Wang, Dongyong; Zhang, Lei; Nie, Qing Array-representation integration factor method for high-dimensional systems. (English) Zbl 1349.65401 J. Comput. Phys. 258, 585-600 (2014). MSC: 65M20 65M12 35K57 PDFBibTeX XMLCite \textit{D. Wang} et al., J. Comput. Phys. 258, 585--600 (2014; Zbl 1349.65401) Full Text: DOI
Ovadia, Jeremy; Nie, Qing Numerical methods for two-dimensional stem cell tissue growth. (English) Zbl 1283.92022 J. Sci. Comput. 58, No. 1, 149-175 (2014). MSC: 92C37 92C15 35Q92 92-08 PDFBibTeX XMLCite \textit{J. Ovadia} and \textit{Q. Nie}, J. Sci. Comput. 58, No. 1, 149--175 (2014; Zbl 1283.92022) Full Text: DOI
Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing A robust and efficient method for steady state patterns in reaction-diffusion systems. (English) Zbl 1250.35017 J. Comput. Phys. 231, No. 15, 5062-5077 (2012). MSC: 35A35 35K57 65M12 35K51 35B36 PDFBibTeX XMLCite \textit{W.-C. Lo} et al., J. Comput. Phys. 231, No. 15, 5062--5077 (2012; Zbl 1250.35017) Full Text: DOI
Lei, Jinzhi; Wan, Frederic Y. M.; Lander, Arthur D.; Nie, Qing Robustness of signaling gradient in drosophila wing imaginal disc. (English) Zbl 1223.92009 Discrete Contin. Dyn. Syst., Ser. B 16, No. 3, 835-866 (2011). MSC: 92C37 92C15 35Q92 34B60 34B15 93B52 65C20 65N99 PDFBibTeX XMLCite \textit{J. Lei} et al., Discrete Contin. Dyn. Syst., Ser. B 16, No. 3, 835--866 (2011; Zbl 1223.92009) Full Text: DOI
Zhao, Su; Ovadia, Jeremy; Liu, Xinfeng; Zhang, Yong-Tao; Nie, Qing Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems. (English) Zbl 1220.65120 J. Comput. Phys. 230, No. 15, 5996-6009 (2011). MSC: 65M06 35K57 65M12 PDFBibTeX XMLCite \textit{S. Zhao} et al., J. Comput. Phys. 230, No. 15, 5996--6009 (2011; Zbl 1220.65120) Full Text: DOI
Liu, Xinfeng; Nie, Qing Compact integration factor methods for complex domains and adaptive mesh refinement. (English) Zbl 1194.65111 J. Comput. Phys. 229, No. 16, 5692-5706 (2010). MSC: 65M20 65M12 35K57 65Y20 65M50 65L05 PDFBibTeX XMLCite \textit{X. Liu} and \textit{Q. Nie}, J. Comput. Phys. 229, No. 16, 5692--5706 (2010; Zbl 1194.65111) Full Text: DOI Link
Liu, Xinfeng; Nie, Qing Spatially-localized scaffold proteins may facilitate to transmit long-range signals. (English) Zbl 1201.92028 Acta Math. Sci., Ser. B, Engl. Ed. 29, No. 6, 1657-1669 (2009). MSC: 92C37 92C40 92C55 35K57 65M06 PDFBibTeX XMLCite \textit{X. Liu} and \textit{Q. Nie}, Acta Math. Sci., Ser. B, Engl. Ed. 29, No. 6, 1657--1669 (2009; Zbl 1201.92028) Full Text: DOI
Lander, A. D.; Nie, Q.; Wan, F. Y. M.; Zhang, Y.-T. Localized ectopic expression of Dpp receptors in a Drosophila embryo. (English) Zbl 1167.92003 Stud. Appl. Math. 123, No. 2, 175-214 (2009). MSC: 92C15 35K57 65C20 65M99 PDFBibTeX XMLCite \textit{A. D. Lander} et al., Stud. Appl. Math. 123, No. 2, 175--214 (2009; Zbl 1167.92003) Full Text: DOI Link
Cai, A. Q.; Peng, Y.; Wells, J.; Dai, X.; Nie, Q. Multi-scale modelling for threshold dependent differentiation. (English) Zbl 1167.92010 Math. Model. Nat. Phenom. 4, No. 4, 103-117 (2009). MSC: 92C37 35Q92 35L60 PDFBibTeX XMLCite \textit{A. Q. Cai} et al., Math. Model. Nat. Phenom. 4, No. 4, 103--117 (2009; Zbl 1167.92010) Full Text: DOI EuDML
Iron, David; Syed, Adeela; Theisen, Heidi; Naghibi, Mehrangiz; Lukacsovich, Tamas; Marsh, Lawrence J.; Wan, Frederic Y. M.; Nie, Qing The role of feedback in the formation of morphogen territories. (English) Zbl 1157.93310 Math. Biosci. Eng. 5, No. 2, 277-298 (2008). MSC: 93A30 35K57 93C95 92D15 93C20 37D45 PDFBibTeX XMLCite \textit{D. Iron} et al., Math. Biosci. Eng. 5, No. 2, 277--298 (2008; Zbl 1157.93310) Full Text: DOI
Nie, Qing; Wan, Frederic Y. M.; Zhang, Yong-Tao; Liu, Xin-Feng Compact integration factor methods in high spatial dimensions. (English) Zbl 1142.65072 J. Comput. Phys. 227, No. 10, 5238-5255 (2008). MSC: 65M06 35K57 PDFBibTeX XMLCite \textit{Q. Nie} et al., J. Comput. Phys. 227, No. 10, 5238--5255 (2008; Zbl 1142.65072) Full Text: DOI Link
Zhang, Yong-Tao; Lander, Arthur D.; Nie, Qing Computational analysis of BMP gradients in dorsal-ventral patterning of the zebrafish embryo. (English) Zbl 1451.92061 J. Theor. Biol. 248, No. 4, 579-589 (2007). MSC: 92C15 92C42 35Q92 92-08 PDFBibTeX XMLCite \textit{Y.-T. Zhang} et al., J. Theor. Biol. 248, No. 4, 579--589 (2007; Zbl 1451.92061) Full Text: DOI Link
Lander, A. D.; Nie, Q.; Wan, F. Y. M. Membrane-associated non-receptors and morphogen gradients. (English) Zbl 1133.92311 Bull. Math. Biol. 69, No. 1, 33-54 (2007). MSC: 92C37 92C40 35K57 PDFBibTeX XMLCite \textit{A. D. Lander} et al., Bull. Math. Biol. 69, No. 1, 33--54 (2007; Zbl 1133.92311) Full Text: DOI Link
Li, Xiangrong; Cristini, Vittorio; Nie, Qing; Lowengrub, John S. Nonlinear three-dimensional simulation of solid tumor growth. (English) Zbl 1124.92022 Discrete Contin. Dyn. Syst., Ser. B 7, No. 3, 581-604 (2007). MSC: 92C50 35Q92 65R20 92C15 65R99 PDFBibTeX XMLCite \textit{X. Li} et al., Discrete Contin. Dyn. Syst., Ser. B 7, No. 3, 581--604 (2007; Zbl 1124.92022) Full Text: DOI
Chou, Ching-Shan; Zhang, Yong-Tao; Zhao, Rui; Nie, Qing Numerical methods for stiff reaction-diffusion systems. (English) Zbl 1125.65080 Discrete Contin. Dyn. Syst., Ser. B 7, No. 3, 515-525 (2007). MSC: 65M06 65M20 35K57 65M12 65M55 PDFBibTeX XMLCite \textit{C.-S. Chou} et al., Discrete Contin. Dyn. Syst., Ser. B 7, No. 3, 515--525 (2007; Zbl 1125.65080) Full Text: DOI
Nie, Qing; Zhang, Yong-Tao; Zhao, Rui Efficient semi-implicit schemes for stiff systems. (English) Zbl 1089.65094 J. Comput. Phys. 214, No. 2, 521-537 (2006). MSC: 65M20 65M06 35K57 65M12 PDFBibTeX XMLCite \textit{Q. Nie} et al., J. Comput. Phys. 214, No. 2, 521--537 (2006; Zbl 1089.65094) Full Text: DOI
Lander, A. D.; Nie, Q.; Wan, F. Y. M. Internalization and end flux in morphogen gradient formation. (English) Zbl 1082.92011 J. Comput. Appl. Math. 190, No. 1-2, 232-251 (2006). MSC: 92C15 92C37 35K57 35Q92 35B35 PDFBibTeX XMLCite \textit{A. D. Lander} et al., J. Comput. Appl. Math. 190, No. 1--2, 232--251 (2006; Zbl 1082.92011) Full Text: DOI
Lander, A. D.; Nie, Q.; Vargas, B.; Wan, F. Y. M. Aggregation of a distributed source in morphogen gradient formation. (English) Zbl 1145.35402 Stud. Appl. Math. 114, No. 4, 343-374 (2005). MSC: 35K57 34B18 35Q80 92B05 92C45 PDFBibTeX XMLCite \textit{A. D. Lander} et al., Stud. Appl. Math. 114, No. 4, 343--374 (2005; Zbl 1145.35402) Full Text: DOI Link
Lou, Yuan; Nie, Qing; Wan, Frederic Y. M. Effects of Sog on Dpp-receptor binding. (English) Zbl 1072.92007 SIAM J. Appl. Math. 65, No. 5, 1748-1771 (2005). MSC: 92C15 92C37 35K57 65C20 92C40 65M06 PDFBibTeX XMLCite \textit{Y. Lou} et al., SIAM J. Appl. Math. 65, No. 5, 1748--1771 (2005; Zbl 1072.92007) Full Text: DOI
Lander, Arthur D.; Nie, Qing; Wan, Frederic Y. M. Spatially distributed morphogen production and morphogen gradient formation. (English) Zbl 1072.92016 Math. Biosci. Eng. 2, No. 2, 239-262 (2005). MSC: 92C40 92C15 35K57 PDFBibTeX XMLCite \textit{A. D. Lander} et al., Math. Biosci. Eng. 2, No. 2, 239--262 (2005; Zbl 1072.92016) Full Text: DOI
Lou, Y.; Nie, Q.; Wan, F. Y. M. Nonlinear eigenvalue problems in the stability analysis of morphogen gradients. (English) Zbl 1141.35465 Stud. Appl. Math. 113, No. 2, 183-215 (2004). MSC: 35Q92 35K50 35K55 35P30 92D10 PDFBibTeX XMLCite \textit{Y. Lou} et al., Stud. Appl. Math. 113, No. 2, 183--215 (2004; Zbl 1141.35465) Full Text: DOI