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Simpsons 1/3 Rule to solve integration

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Mckale Grant
Mckale Grant 2022-2-23
回答： Torsten 2022-2-23
The enthalpy of a real gas is a function of pressure as described below. The data was taken for a real fluid. Estimate and report the enthalpy of the fluid at 400 K and 50 atm (evaluate the integral from 0.1 atm to 50 atm).
My Code:
% Use Simpsons 1/3 Rule to solve integration
% Lower Limit
a = 0.1; % Pressure in atm
% Upper Limit
b = 50; % Pressure in atm
% Number of Segments
n = 9;
% Declare the function
T = 400; % Temp. in K
V = [250 4.7 2.5 1.49 1.20 0.99 0.75 0.675 0.60]; % Volume at T = 400K
% dVdT = V(T = 350) - V(T = 450)/100
dVdT = [0.625 0.0113 0.005 0.002 0.0014 0.0013 0.001 0.0009 0.0008];
H = V-T.*dVdT;
% inline creates a function of string containing in H
f = inline(H);
% h is the segment size
h = (b - a)/n;
% X stores the summation of first and last segment
X = f(a) + f(b);
% variables Odd and Even to store summation of odd and even terms respectively
Odd = 0;
Even = 0;
for i = 1:2:n - 1
xi = a + (i*h);
Odd = Odd + f(xi);
end
for i = 2:2:n - 2
xi = a+(i*h);
Even = Even + f(xi);
end
% Formula to calculate numerical integration using Simpsons 1/3 Rule
I = (h/3)*(X + 4*Odd + 2*Even)
The Error My Code Produces:
Error using inline (line 51)
Input must be a character vector.
Error in HW6_P1 (line 23)
f = inline(H);
Used this to solve function

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回答（2 个）

Cris LaPierre
Cris LaPierre 2022-2-23
As the error states, the input to inline must be a character vector (e.g. f = inline('sin(alpha*x)'))
Note that inline is not recommended. Use Anonymous Functions instead.
Torsten
Torsten 2022-2-23
Be careful here: the pressure values are not equally spaced.
Use
T = 400; % Temp. in K
P = [0.1 5 10 20 25 30 40 45 50]; % Pressure in atm
V = [250 4.7 2.5 1.49 1.20 0.99 0.75 0.675 0.60]; % Volume at T = 400K
% dVdT = V(T = 350) - V(T = 450)/100
dVdT = [0.625 0.0113 0.005 0.002 0.0014 0.0013 0.001 0.0009 0.0008];
H = V-T.*dVdT;
I = trapz(P,H)
to calculate enthalpy at T=400 K and P=50 atm.

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