File "multivariate_newton_raphson_test_code_for_coupled_ode.py" is just a test code to solve some simple system of ordinary differential equations shown below.

dy_1/dt = -0.04y_1 + 10^4y_2*y_3

dy_2/dt = 0.04y_1 - 10^4y_2y_3 - 310^7*(y_2)^2

dy_3/dt = 310^7(y_2)^2

with initial condition y_1(0) = 1, y_2(0) = 0, y_3(0) = 0 over t = [0, 600] in seconds.