I am working with a nonlinear system of equations, where the term ( left| frac{partial phi_2′}{partial r} right| ) appears in the equations. I need to solve the system iteratively and compare the coefficients calculated using the initial assumption (with ( left| frac{partial phi_2′}{partial r} right| = 0 ) at first) with the updated coefficients obtained after several iterations.

The steps of the process are as follows:

begin{itemize}
item textbf{Step A:} Assume that the value of ( left| frac{partial phi_2′}{partial r} right| ) is known (set to 0 initially) and the coefficients ( c_n, c_n^-, d^0, d_n^+, d_n^- ) are unknown. The system of equations becomes linear and can be solved by Gaussian elimination.

item textbf{Step B:} After obtaining the initial solution, substitute the value of ( left| frac{partial phi_2′}{partial r} right| ) into the equation set and solve for all unknown coefficients, and update the value of ( left| frac{partial phi_2′}{partial r} right| ).

item textbf{Step C:} Calculate the updated unknown coefficients, and compare them with the values obtained in the previous iteration. If the difference between any coefficient is smaller than ( 10^{-3} ), stop the iteration and consider the solution as the final result. Otherwise, continue iterating, updating the value of ( left| frac{partial phi_2′}{partial r} right| ) in each step.
end{itemize}

How can I implement this iterative solution in MATLAB? Specifically, how can I calculate and compare the differences between the unknown coefficients obtained in each step using the initial and updated values of ( left| frac{partial phi_2′}{partial r} right| )?I am working with a nonlinear system of equations, where the term ( left| frac{partial phi_2′}{partial r} right| ) appears in the equations. I need to solve the system iteratively and compare the coefficients calculated using the initial assumption (with ( left| frac{partial phi_2′}{partial r} right| = 0 ) at first) with the updated coefficients obtained after several iterations.

The steps of the process are as follows:

begin{itemize}
item textbf{Step A:} Assume that the value of ( left| frac{partial phi_2′}{partial r} right| ) is known (set to 0 initially) and the coefficients ( c_n, c_n^-, d^0, d_n^+, d_n^- ) are unknown. The system of equations becomes linear and can be solved by Gaussian elimination.

item textbf{Step B:} After obtaining the initial solution, substitute the value of ( left| frac{partial phi_2′}{partial r} right| ) into the equation set and solve for all unknown coefficients, and update the value of ( left| frac{partial phi_2′}{partial r} right| ).

item textbf{Step C:} Calculate the updated unknown coefficients, and compare them with the values obtained in the previous iteration. If the difference between any coefficient is smaller than ( 10^{-3} ), stop the iteration and consider the solution as the final result. Otherwise, continue iterating, updating the value of ( left| frac{partial phi_2′}{partial r} right| ) in each step.
end{itemize}

How can I implement this iterative solution in MATLAB? Specifically, how can I calculate and compare the differences between the unknown coefficients obtained in each step using the initial and updated values of ( left| frac{partial phi_2′}{partial r} right| )? I am working with a nonlinear system of equations, where the term ( left| frac{partial phi_2′}{partial r} right| ) appears in the equations. I need to solve the system iteratively and compare the coefficients calculated using the initial assumption (with ( left| frac{partial phi_2′}{partial r} right| = 0 ) at first) with the updated coefficients obtained after several iterations.

The steps of the process are as follows:

begin{itemize}
item textbf{Step A:} Assume that the value of ( left| frac{partial phi_2′}{partial r} right| ) is known (set to 0 initially) and the coefficients ( c_n, c_n^-, d^0, d_n^+, d_n^- ) are unknown. The system of equations becomes linear and can be solved by Gaussian elimination.

item textbf{Step B:} After obtaining the initial solution, substitute the value of ( left| frac{partial phi_2′}{partial r} right| ) into the equation set and solve for all unknown coefficients, and update the value of ( left| frac{partial phi_2′}{partial r} right| ).

item textbf{Step C:} Calculate the updated unknown coefficients, and compare them with the values obtained in the previous iteration. If the difference between any coefficient is smaller than ( 10^{-3} ), stop the iteration and consider the solution as the final result. Otherwise, continue iterating, updating the value of ( left| frac{partial phi_2′}{partial r} right| ) in each step.
end{itemize}

How can I implement this iterative solution in MATLAB? Specifically, how can I calculate and compare the differences between the unknown coefficients obtained in each step using the initial and updated values of ( left| frac{partial phi_2′}{partial r} right| )? linear, system, equation, iteration MATLAB Answers — New Questions

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