Skip to main content

Theory and Modern Applications

Figure 5 | Advances in Difference Equations

Figure 5

From: Numerical study and stability of the Lengyel–Epstein chemical model with diffusion

Figure 5

(a)–(d) Numerical solutions of system (49) using Crank–Nicolson scheme. Here, \(u_{0} = 1 + \sin (x)\) and \(v_{0} = 2 + \cos (x)\), with \(l = 5\), \(m = 1\), \(\kappa_{1} =0.01\), and \(\kappa_{2} =0.01\). (Top) The concentration of \(u(\tau )\) is on the left while the concentration of \(v(\tau )\) is on the right. (Bottom) The solutions \(v(x,\tau )\) and \(u(x,\tau )\) tend to the constant steady state. (e)–(h) Numerical solutions of system (49) using Crank–Nicolson scheme. Here, \(u_{0} = 1 + \sin (x)\) and \(v_{0} = 2 + \cos (x)\), with \(l = 10\), \(m = 20\), \(\kappa_{1} =0.01\), and \(\kappa_{2} =0.01\). (Top) The solutions \(v(x,\tau )\) and \(u(x,\tau )\) tend to the spatially nonhomogeneous steady states. (Bottom) The projected views onto the -plane at \(\tau=20\) for \(v(x,\tau )\) and \(u(x,\tau )\). The stripe structure invades the nonhomogeneous steady states for \(v(x,\tau )\) and \(u(x,\tau )\)

Back to article page