1. Abedian, R., Adibi, H., and Dehghan, M. A high-order symmetrical weighted hybrid ENO-flux limiter scheme for hyperbolic conservation laws, Comput. Phys. Commun. 185 (2014), no. 1, 106–127.
2. Abedian, R., Adibi, H., and Dehghan, M. A high-order weighted essentially non-oscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations, Comput. Phys. Commun. 184 (2013), no. 8, 1874–1888.
3. Acosta, C. D. and B¨urger, R. Difference schemes stabilized by discrete mollification for degenerate parabolic equations in two space dimensions, IMA J. Numer. Anal. 32 (2012), no, 4, 1509–1540.
4. Aregba-Driollet, D., Natalini, R., and Tang, S. Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems, Math. Comp. 73(2004), no. 245. 63–94.
5. Barenblatt, G. I. On some unsteady motions of a liquid or a gas in a porous medium, (Russian) Akad. Nauk SSSR. Prikl. Mat. Meh. 16, (1952). 67–78.
6. Barenblatt, G. I., Bertsch, M., Chertock, A. E., and Prostokishin, V. M. Self-similar intermediate asymptotics for a degenerate parabolic filtration absorption equation, Proc. Natl. Acad. Sci. U.S.A. 97 (2000), no. 18, 9844–9848.
7. Bendahmane, M., B¨urger, R., Ruiz-Baier, R., and Schneider, K. Adaptive multiresolution schemes with local time stepping for two-dimensional degenerate reaction-diffusion systems, Appl. Numer. Math. 59 (2009), no. 7,1668–1692.
8. Capdeville, G. A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes, J. Comput. Phys, 227 (2008), no. 5, 2977–3014.
9. Cavalli, F., Naldi, G., Puppo, G., and Semplice, M. High order relax ation schemes for nonlinear degenerate diffusion problems, SIAM J. Numer. Anal. 45 (2007), no. 5, 2098–2119.
10. Cockburn, B. and Shu, C. -W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM J. Numer. Anal. 35 (1998), no. 6, 2440–2463.
11. Davidovitch, B., Moro, E., and Stone, A. H. Spreading of viscous fluid drops on a solid substrate assisted by thermal fluctuations, Phys. Rev. Lett. 95 (2005), no. 24, 244–505.
12. Fedkiw, R., Merriman, B., and Osher, S. Simplified discretization of sys tems of hyperbolic conservation laws containing advection equations, J. Comput. Phys. 157 (2000), no. 1, 302–326.
13. Friedrichs, K. O. and Lax, P. D. Systems of conservation equations with a convex extension, Proc. Natl. Acad. Sci. U.S.A. 68 (1971), 1686–1688.
14. Gierer, A. and Meinhardt, H. A theory of biological pattern formation, Biol. Cybern. 12 (1972), no. 1, 30–39.
15. Hajipour, M. and Malek, A. High accurate NRK and MWENO scheme for nonlinear degenerate parabolic PDEs, Appl. Math. Model. 36 (2012), no. 9, 4439–4451.
16. Harley, C. Asymptotic and dynamical analyses of heat transfer through a rectangular longitudinal fin, J. Appl. Math. 2013, Art. ID 987327, 1–8.
17. Harten, A., Engquist, B., Osher, S., and Chakravarthy, S. Uniformly high-order essentially nonoscillatory schemes, III, J. Comput. Phys. 71 (1987), no. 2, 231–303.
18. Harten, A. and Osher, S. Uniformly high-order accurate nonoscillatory schemes I, SIAM J. Numer. Anal. 24 (1987), no. 2, 279–309.
19. Henrick, A. K., Aslam, T. D., and Powers, J. M. Mapped weighted essen tially nonoscillatory schemes: Achieving optimal order near critical points, J. Comput. Phys. 207 (2005), no. 2, 542–567.
20. Holden, H., Karlsen, K. H., and Lie, K. -A. Operator splitting methods for degenerate convection-diffusion equations II: Numerical examples with emphasis on reservoir simulation and sedimentation, Comput. Geosci. 4(2000), 287–322.
21. Jiang, G. S. and Shu, C. -W. Efficient implementation of weighted ENOschemes, J. Comput. Phys. 126 (1996), no. 1, 202–228.
22. Karlsen, K. H. and Risebro, N. H. An operator splitting method for nonlinear convection-diffusion equations, Numer. Math. 77 (1997), no. 3, 365–382.
23. Kurganov, A. and Tadmor, E. New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000), no. 1, 241–282.
24. Levy, D., Puppo, G., and Russo, G. Compact central WENO schemes for multidimensional conservation laws, SIAM J. Sci. Comput. 22 (2000), no. 2, 656–672.
25. Liu, X. -D., Osher, S., and Chan, T. Weighted essentially non-oscillatory schemes, J. Comput. Phys. 115 (1994), no. 1, 200–212.
26. Liu, Y., Shu, C. -W., and Zhang, M. High order finite difference WENO schemes for nonlinear degenerate parabolic equations, SIAM J. Sci. Comput. 33 (2011), no. 2, 939–965.
27. Maini, P. K., Woolley, T. E., Baker, R. E., Gaffney, E. A., and Lee, S. S. Turing’s model for biological pattern formation and the robustness problem, Interface focus 2 (2012), no. 4, 487–496.
28. Murray, J. D. Mathematical Biology II: Spatial Models and Biomedical Applications, Springer-Verlag, New York, 2003.
29. Nessyahu, H. and Tadmor, E. nonoscillatory central differencing for hyperbolic conservation laws, J. omput. Phys. 87 (1990), no. 2, 408–463.
30. Peer, A. A. I., Dauhoo, M. Z., Gopaul, A., and Bhuruth, M. A weighted ENO-flux limiter scheme for hyperbolic conservation laws, Int. J. Comput. Math. 87 (2010), no. 15, 3467–3488.
31. Schnakenberg, J. Simple chemical reaction systems with limit cycle behaviour, J. Theoret. Biol. 81 (1979), no. 3, 389–400.
32. Shu, C. -W. Essentially non-oscillatory and weighted essentially nonoscillatory schemes for hyperbolic conservation laws, Advanced numerical approximation of nonlinear hyperbolic equations (Cetraro, 1997), 325–432, Lecture Notes in Math., 1697, Fond. CIME/CIME Found. Subser., Springer, Berlin, 1998.
33. Shu, C. -W. and Osher, S. Efficient implementation of essentially nonoscillatory shock-capturing schemes, J. Comput. Phys. 77 (1988), no. 2, 439–471.
34. Turing, M. A. The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. London Ser. B 237 (1952), no. 641, 37–72.
35. van Leer, B. Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov’s method, J. Comput. Phys. 32 (1979), no. 1, 101–136.
36. V´azquez, J. L. The Porous Medium Equation: Mathematical Theory, Oxford University Press, USA, 2007.
37. Witelski, T. P. Segregation and mixing in degenerate diffusion in popu lation dynamics, J. Math. Biol. 35 (1997), no. 6, 695–712.
38. Zel’dovich, Y. B. and Kompaneetz, A. S. Towards a theory of heat con duction with thermal conductivity depending on the temperature, in: Col lection of Papers Dedicated to 70th Birthday of Academician A.F. Ioffe, Izd. Akad. Nauk SSSR, Moscow, 1950, pp. 61–71.
39. Zhang, Q. and Wu, Z. -L. Numerical simulation for porous medium equa tion by local discontinuous Galerkin finite element method. J. Sci. Comput. 38 (2009), no. 2, 127–148.
