Create ODE_Nonlinear_system_of_reactions_with_an_analytical_solution

Author: EdelmanJonathan

src/ode/ODE_Nonlinear_system_of_reactions_with_an_analytical_solution

@@ -0,0 +1,28 @@
+using DifferentialEquations
+using Plots
+using SpecialFunctions
+
+function nonLinChem(dy,y,p,t)
+ dy[1] = -y[1]
+ dy[2] = y[1]-(y[2])^2
+ dy[3] = (y[2])^2
+end
+y0 = [1.0;0.0;0.0]
+tspan = (0.0,20)
+prob = ODEProblem(nonLinChem,y0,tspan)
+sol = solve(prob)
+
+Analytical(t) = [exp(-t);
+    (2sqrt(exp(-t))besselk(1,2sqrt(exp(-t)))-2besselk(1,2)/besseli(1,2)*sqrt(exp(-t))besseli(1,2sqrt(exp(-t))))/(2besselk(0,2sqrt(exp(-t)))+(2besselk(1,2)/besseli(1,2))besseli(0,2sqrt(exp(-t))));
+    -exp(-t)+1+(-2sqrt(exp(-t))*besselk(1,2sqrt(exp(-t)))+sqrt(exp(-t))*besseli(1,2sqrt(exp(-t)))*2besselk(1,2)/besseli(1,2))/(2besselk(0,2sqrt(exp(-t)))+2besselk(1,2)/besseli(1,2)*besseli(0,2sqrt(exp(-t))))]
+
+t=0:.1:20
+p = 1
+plot(sol,vars=(0,p))
+plot!(t,(x->Analytical(x)[p]).(t))
+p = 2
+plot!(sol,vars=(0,p))
+plot!(t,(x->Analytical(x)[p]).(t))
+p = 3
+plot!(sol,vars=(0,p))
+plot!(t,(x->Analytical(x)[p]).(t))