Need pyhton program code for LCR circuit, modeled

with differential equations, and solve it using two numerical methods: the explicit Euler Method and a third$-$order Runge$-$Kutta method. By comparing the results, you$$ll

gain insights into the accuracy and efficiency of each method.

Tasks:

$$ Select a physical system: This could be anything from a bouncing ball to

a swinging pendulum, a rocket launch to a predator$-$prey model. Be sure the

system can be described by a first$-$order system of ordinary differential equations

$($ODE$).$ Be ambitious in choosing the physical system as the grade depends on

it$.$

$$ Identify relevant variables: Define the key variables involved in your chosen

system. For example, for a bouncing ball, these could be its position and velocity.

$$ Implement the Euler Method: Implement the Euler Method: Use the Euler

method to solve your chosen ODE numerically. Remember this method requires

choosing a step size and iteratively updating the values of your variables accord

ing to the defined function.

$$ Implement a Third$-$Order Runge$-$Kutta Method: Implement a third$-$order

Runge$-$Kutta method, which uses several evaluations of the function per step to

achieve higher accuracy.

$$ Programyoursolutions: ChoosePythonasyourprogrammingandwritescripts

to implement both methods. Make sure your code is well$-$structured, docu

mented, and easy to understand.

$$ Run simulations: Execute your code for both methods with different initial

conditions and step sizes. Plot the obtained solutions over time.

$$ Compare accuracy: Analyze the difference between the solutions obtained

from each method. Use error metrics like absolute error or relative error to quan

tify the discrepancies.

$$ Explore efficiency: Compare the computation time required by each method for

different step sizes. Analyze how computational effort affects accuracy.

Discuss limitations: Discuss the limitations of each method, such as order of accuracy and stability. Explain scenarios where one method might be preferable

over the other