Nested For Loop/Newton Raphson
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I am trying to run carry out the Newton Raphson method for a series of Area Ratios in relation to Wind Tunnel experiments. x0 is an initial guess and the AR is an array of 25 area ratios. The method will converge on a solution. I need the for loop to run through all of the area ratios and calculate an X value for each, and return this in the array M for each ratio. Unfortunately I cant get this to work and will just repeat the same X value for all of the ratios at the end. Does anyone have any ideas how I could fix this?
x0 = 1.5; %x0 represents Mach Number Initial Guess
AR = [1.8652 1.5472 1.3327 1.1793 1.0827 1.0258 1.0016 1.0302 1.1091 1.1898 1.2653 1.3334 1.392 1.4389 1.4759 1.5044 1.5249 1.5376 1.5467 1.5547 1.5626 1.5704 1.5783 1.5862 1.5941]
f = @(x0) ((((5/6)+((1/6)*(x0^2)))^3))-(x0*AR);
df = @(x0)((x0))*(((5/6)+((1/6)*(x0^2)))^2)-AR;
M = [];
for i=AR
for i=1:10
x1 = x0 - f(x0)/df(x0);
x0 = x1;
disp(x1)
end
M=[M,(x1)];
end
Answers (1)
x0 = 1.5; %x0 represents Mach Number Initial Guess
AR = [1.8652 1.5472 1.3327 1.1793 1.0827 1.0258 1.0016 1.0302 1.1091 1.1898 1.2653 1.3334 1.392 1.4389 1.4759 1.5044 1.5249 1.5376 1.5467 1.5547 1.5626 1.5704 1.5783 1.5862 1.5941]
f = @(x0) ((((5/6)+((1/6)*(x0.^2))).^3))-(x0.*AR);
df = @(x0)((x0)).*(((5/6)+((1/6)*(x0.^2))).^2)-AR;
for k=1:length(AR)
x1 = x0 - f(x0)./df(x0);
x0 = x1;
disp(x1);
M{k}=x1;
end
M.'
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on 14 Dec 2022
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