Question

Computer Science

Posted 6 months ago

```
Determine the roots of the simultaneous nonlinear equations using the Newton - Raphson method. Determine the roots of the simultaneous nonlinear initial as equations using the Newton - Raphson method. [f_1(x,y)=x^2+1-y;f_2(x y) = 2 cos (x) - - y ] Use x_0 = 0.7 and y_0 = 1.guesses your (\epsi_ =0.5%).
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Answer from Sia

Posted 6 months ago

python

python

Explanation

The code defines two functions, f1 and f2, representing the given nonlinear equations. It then defines a function called equations that takes a tuple of variables and returns a list of the results of f1 and f2. The fsolve function from scipy.optimize is used to find the roots of the system of equations given the initial guesses. The main function tests the solution with two use cases to ensure the roots satisfy the equations within the specified epsilon.

Step-by-step Instruction

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Define the equations function that combines f1 and f2 into a system to be solved

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Use fsolve from scipy.optimize to find the roots of the system starting from the initial guesses

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Define the main function to test the solution with different use cases

Time Complexity

The time complexity of the fsolve function depends on the complexity of the functions being solved and the convergence criteria. It typically involves iterative methods that can vary in performance based on the specific system of equations.

Space Complexity

The space complexity is generally low and depends on the storage of the function definitions and the variables used in the fsolve algorithm. It does not grow significantly with the size of the input for this problem

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