Van Gorder, Robert A.; Kim, Hyunyeon; Krause, Andrew L. Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains. (English) Zbl 1430.76176 J. Fluid Mech. 877, 759-823 (2019). MSC: 76E06 76V05 35K57 76D07 PDFBibTeX XMLCite \textit{R. A. Van Gorder} et al., J. Fluid Mech. 877, 759--823 (2019; Zbl 1430.76176) Full Text: DOI
Kleanthous, Antigoni; Hua, Tianshu; Manai, Alexandre; Yawar, Kamran; Van Gorder, Robert A. Dynamics from a mathematical model of a two-state gas laser. (English) Zbl 1514.35422 Physica A 497, 26-40 (2018). MSC: 35Q60 35B30 35C07 78A60 PDFBibTeX XMLCite \textit{A. Kleanthous} et al., Physica A 497, 26--40 (2018; Zbl 1514.35422) Full Text: DOI Link
Bhrawy, A. H.; Doha, E. H.; Abdelkawy, M. A.; Van Gorder, Robert A. Jacobi-Gauss-Lobatto collocation method for solving nonlinear reaction-diffusion equations subject to Dirichlet boundary conditions. (English) Zbl 1446.65124 Appl. Math. Modelling 40, No. 3, 1703-1716 (2016). MSC: 65M70 35K20 35K57 PDFBibTeX XMLCite \textit{A. H. Bhrawy} et al., Appl. Math. Modelling 40, No. 3, 1703--1716 (2016; Zbl 1446.65124) Full Text: DOI
Doha, Eid H.; Bhrawy, Ali H.; Hafez, Ramy M.; Van Gorder, Robert A. Jacobi rational-Gauss collocation method for Lane-Emden equations of astrophysical significance. (English) Zbl 1423.85007 Nonlinear Anal., Model. Control 19, No. 4, 537-550 (2014). MSC: 85A15 35Q85 PDFBibTeX XMLCite \textit{E. H. Doha} et al., Nonlinear Anal., Model. Control 19, No. 4, 537--550 (2014; Zbl 1423.85007) Full Text: DOI
Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.; van Gorder, Robert A. A Jacobi rational pseudospectral method for Lane-Emden initial value problems arising in astrophysics on a semi-infinite interval. (English) Zbl 1308.85006 Comput. Appl. Math. 33, No. 3, 607-619 (2014). MSC: 85A15 34B16 33C45 34A25 65N35 PDFBibTeX XMLCite \textit{E. H. Doha} et al., Comput. Appl. Math. 33, No. 3, 607--619 (2014; Zbl 1308.85006) Full Text: DOI
Baxter, Mathew; van Gorder, Robert A.; Vajravelu, Kuppalapalle On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem. (English) Zbl 1293.65137 Numer. Algorithms 66, No. 2, 269-298 (2014). MSC: 65M99 65M12 65K10 49J20 35Q35 PDFBibTeX XMLCite \textit{M. Baxter} et al., Numer. Algorithms 66, No. 2, 269--298 (2014; Zbl 1293.65137) Full Text: DOI
Reger, K.; Van Gorder, R. A. Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere. (English) Zbl 1284.80008 Appl. Math. Mech., Engl. Ed. 34, No. 12, 1439-1452 (2013). MSC: 80A25 34A34 34D10 34A25 PDFBibTeX XMLCite \textit{K. Reger} and \textit{R. A. Van Gorder}, Appl. Math. Mech., Engl. Ed. 34, No. 12, 1439--1452 (2013; Zbl 1284.80008) Full Text: DOI
Hearns, Jessica; Van Gorder, Robert A.; Choudhury, S. Roy Painlevé test, integrability, and exact solutions for density-dependent reaction-diffusion equations with polynomial reaction functions. (English) Zbl 1309.35040 Appl. Math. Comput. 219, No. 6, 3055-3064 (2012). MSC: 35K57 35C05 PDFBibTeX XMLCite \textit{J. Hearns} et al., Appl. Math. Comput. 219, No. 6, 3055--3064 (2012; Zbl 1309.35040) Full Text: DOI
Van Gorder, Robert A. Control of error in the homotopy analysis of semi-linear elliptic boundary value problems. (English) Zbl 1257.65063 Numer. Algorithms 61, No. 4, 613-629 (2012). MSC: 65N15 35J61 65N99 65N12 PDFBibTeX XMLCite \textit{R. A. Van Gorder}, Numer. Algorithms 61, No. 4, 613--629 (2012; Zbl 1257.65063) Full Text: DOI
Haussermann, John; Van Gorder, Robert A. Asymptotic solutions for singularly perturbed Boussinesq equations. (English) Zbl 1246.35174 Appl. Math. Comput. 218, No. 20, 10238-10243 (2012). MSC: 35Q51 35D30 35C11 PDFBibTeX XMLCite \textit{J. Haussermann} and \textit{R. A. Van Gorder}, Appl. Math. Comput. 218, No. 20, 10238--10243 (2012; Zbl 1246.35174) Full Text: DOI
Sweet, Erik; Van Gorder, Robert A. Traveling wave solutions \((u,\nu)\) to a generalized Drinfel’d-Sokolov system which satisfy \(u=a_1\nu^m+a_0\). (English) Zbl 1252.65177 Appl. Math. Comput. 218, No. 19, 9911-9921 (2012). MSC: 65M99 PDFBibTeX XMLCite \textit{E. Sweet} and \textit{R. A. Van Gorder}, Appl. Math. Comput. 218, No. 19, 9911--9921 (2012; Zbl 1252.65177) Full Text: DOI
Van Gorder, Robert A. Analytical solutions to a quasilinear differential equation related to the Lane-Emden equation of the second kind. (English) Zbl 1270.85006 Celest. Mech. Dyn. Astron. 109, No. 2, 137-145 (2011). MSC: 85A05 76N15 PDFBibTeX XMLCite \textit{R. A. Van Gorder}, Celest. Mech. Dyn. Astron. 109, No. 2, 137--145 (2011; Zbl 1270.85006) Full Text: DOI
Sweet, Erik; Van Gorder, Robert A. Trigonometric and hyperbolic type solutions to a generalized Drinfel’d-Sokolov equation. (English) Zbl 1206.35223 Appl. Math. Comput. 217, No. 8, 4147-4166 (2010). MSC: 35Q53 35C09 35B30 35A35 35C20 PDFBibTeX XMLCite \textit{E. Sweet} and \textit{R. A. Van Gorder}, Appl. Math. Comput. 217, No. 8, 4147--4166 (2010; Zbl 1206.35223) Full Text: DOI
Sweet, Erik; Van Gorder, Robert A. Analytical solutions to a generalized Drinfel’d-Sokolov equation related to DSSH and KdV6. (English) Zbl 1195.35271 Appl. Math. Comput. 216, No. 10, 2783-2791 (2010). MSC: 35Q53 35B20 35B30 35A22 35A35 35C05 PDFBibTeX XMLCite \textit{E. Sweet} and \textit{R. A. Van Gorder}, Appl. Math. Comput. 216, No. 10, 2783--2791 (2010; Zbl 1195.35271) Full Text: DOI