Scientific Calculations with Julia/Electrical Circuits

Scientific Calculations with Julia Electrical Circuits Big Bang Diagnosing Heart Disease Example 1 Given the following linear circuit, we want to determine the values ​​of the currents : Applying Kirchoff's laws, we obtain a linear system of three equations in three unknowns: If the data are as follows: : You can solve the system with Julia: A=[-1 1 1;13 0 20;0 2 -20] 3×3 Matrix{Int64}: -1 1 1 13 0 20 0 2 -20 b=[0, 40, -20] 3-element Vector{Int64}: 0 40 -20 A\b 3-element Vector{Float64}: 1.4723926380368098 0.4294478527607364 1.0429447852760736 So we get: Example 2 Given the following second-order linear circuit, we want to determine The values ​​of the voltages and currents : thumb|center|300px Applying Kirchoff's laws yields a linear system of three equations in three unknowns: If the data are as follows: we obtain the system of differential equations: with initial conditions: Solving this system with Julia gives: function ode_fn(du,u,p,t) x, y = u du[1] = -4 - x/5- y/5 du[2] = x/5 - y/5 end using DifferentialEquations using Plots t_begin=0.0 t_end=30 tspan = (t_begin,t_end) x_init=10.0 y_init=10.0 prob = ODEProblem(ode_fn, [x_init, y_init], tspan) num_sol = solve(prob, Tsit5(), reltol=1e-8, abstol=1e-8) x_num_sol = [u[1] for u in num_sol.u] y_num_sol = [u[2] for u in num_sol.u] plot(num_sol.t, x_num_sol, title="Tensione su C e corrente su L", xaxis="t", linewidth=2, label="Tensione su C") plot!(num_sol.t, y_num_sol, linewidth=2, label="Corrente su L") thumb|center|500px