Draw figures of the numerical results with respect to the above three methods in phase space, respectively,
Consider the initial value problem dudt=u(v−2) :=a(u, v),dvdt=v(1−u) :=b(u, v),u(0) =u0, v(0) =v0,(0.2)wheret >0. Let stepsizeh= 0.1. Solve (0.2) by using thefollowing three methods:(a) Explicit Euler method with (u0, v0) = (1,1)∂(b) Implicit Euler method with (u0, v0) = (4,4)∂(c)un+1=un+ha(un, vn+1),vn+1=vn+hb(un, vn+1),(u0, v0) = (5,2).(0.3)Draw figures of the numerical results with respect to the abovethree […]