Concept explainers
Recall from Sec. 8.2 that determining the chemistry of water exposed to atmospheric
To calculate: The solutions of the system offive nonlinear equations (refer section 8.2) given by,
And, to compute the
Answer to Problem 21P
Solution: The solution to the system of five nonlinear equations is
The
Explanation of Solution
Given Information:
The system offivesimultaneousnonlinear equations,
Here,
The values of constants
Consider, the value of partial pressure of
Formula used:
For system of n simultaneous nonlinear equations formulated as,
From Newton-Raphson method, for
Here,
Further, the above equation is rewritten as,
Write the matrix equation for partial derivatives.
Initial and the final values are expressed as,
And,
Write the function values at
Thus, simplify the partial derivative equation as,
The above equation can then be solved iteratively to obtain the solutions to the system of nonlinear equations.
Calculation:
Apply a technique based on Newton-Raphson method to solve the system of nonlinear equations.
Use the following MATLAB code toimplement Newton Raphson method and solve the given system of simultaneous nonlinear equations.
function
[
end
function[
if
if
if
while(
[
if
end
end
function[
end
function
end
function
end
function
end
function
end
function
end
Execute the above code to obtain the solutions as,
Hence, the solution to the system of five nonlinear equations is
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