Using a function and fsolve with a for loop

I'd like to solve the system of 4 non linear equations and 4 unknonws over a span of values for T.

I'm recieving the following error:

"This statement is not inside any function.

(It follows the END that terminates the definition of the function "eqn".)"

function F = eqn(x,T)
F(1) = 10.*(T-x(1))+0.2.*(T.^4-x(1).^4) - x(4);
F(2) = -1.*(1/x(1)-1/x(2)) - x(4);
F(3) = 2.*(x(3)-x(2))-x(4);
F(4) = 5.*(1-x(3))-x(4);
end
T = 1:1:40;
for i = 1:numel(T)
    x(i,:)=fsolve(@(x)eqn(x,T(i)),[0,0,0,0]);
end

Answer 1

[Steven Lord]

Either remove the section of code starting with "T = 1:1:40;" from your function file and run it in the Command Window or another file, or move that section of code to before the line "function F = eqn(x,T)". This second approach may require you to change the name of your function or the name of the file that contains it.

[Tony Stianchie]

Removing the section of code starting with "T=1:1:40" and running in a seperate file results in the following error:

Error using trustnleqn (line 28)

Objective function is returning undefined values at initial point. FSOLVE cannot continue.

Error in fsolve (line 414)

trustnleqn(funfcn,x,verbosity,gradflag,options,defaultopt,f,JAC,...

[Torsten]

Yes, you divide by 0 in the expressions 1/x(1) and 1/x(2) if you set [0 0 0 0] as initial guess.

[Alex Sha]

See the results below:

T	x1	x2	x3	x4
1	1	1	1	-4.41868100791151E-15
2	-0.04221805467944030	-15.5355259373919	-3.72443598211183	23.6221799105584
3	-0.02152989066740660	-31.4907092033764	-8.28305977239318	46.4152988619656
4	-0.01094985711415290	-62.9166489977652	-17.2618997136447	91.309498568229
5	-0.00571215265706289	-121.539985068469	-34.0114243052774	175.057121526389
6	-0.00313248055977908	-222.461927363911	-62.8462649611353	319.231324805659
7	-0.00181745226754944	-384.152722165812	-109.043634904507	550.218174522591
8	-0.00111208392250994	-628.447784587467	-178.842224167857	899.211120839266
9	-0.000713160880548333	-980.544992126182	-279.441426321773	1402.2071316088
10	-0.000476189242038096	-1469.00333332469	-419.000952378488	2100.00476189245
11	-0.000329141847745449	-2125.74230399299	-606.640658283718	3038.20329141854
12	-0.000234345559697521	-2986.04164041889	-852.440468691099	4267.20234345554
13	-0.000171168338151485	-4088.54119817842	-1167.44034233668	5842.20171168344
14	-0.000127824907104757	-5475.2408947744	-1563.64025564984	7823.20127824912
15	-9.73235904377666E-5	-7191.50068126512	-2054.00019464718	10275.0009732358
16	-7.53738494234600E-5	-9286.04052761695	-2652.44015074771	13267.2007537385
17	-5.92620663416646E-5	-11810.9404148345	-3373.84011852413	16874.2005926207
18	-4.72250545218803E-5	-14821.6403305754	-4234.04009445011	21175.2004722506
19	-3.80891432006883E-5	-18376.940266624	-5249.84007617831	26254.2003808915
20	-3.10559002788023E-5	-22539.0002173913	-6439.00006211179	32200.000310559
21	-2.55713925803802E-5	-27373.3401789998	-7820.2400511428	39106.200255714
22	-2.12444126098758E-5	-32948.8401487108	-9413.24004248879	47071.2002124441
23	-1.77941641615093E-5	-39337.7401245591	-11238.6400355883	56198.2001779416
24	-1.50160972175629E-5	-46615.6401051127	-13318.0400300322	66595.2001501609
25	-1.27591706301686E-5	-54861.5000893142	-15674.0000255183	78375.0001275917
26	-1.09104556930710E-5	-64157.6400763732	-18330.0400218209	91655.2001091045
27	-9.38454289762297E-6	-74589.7400656918	-21310.6400187691	106558.200093845
28	-8.11614527938351E-6	-86246.8400568131	-24641.2400162323	123211.200081161
29	-7.05486284239850E-6	-99221.340049384	-28348.2400141097	141746.200070549
30	-6.16142944895955E-6	-113609.00004313	-32459.0000123228	162300.000061614
31	-5.40499053405699E-6	-129508.940037835	-37001.840010810	185014.20005405
32	-4.76110670849903E-6	-147023.640033328	-42006.0400095222	210035.200047611
33	-4.21027458483498E-6	-166258.940029472	-47501.8400084205	237514.200042103
34	-3.73682023443470E-6	-187324.040026158	-53520.4400074736	267607.200037368
35	-3.32806389840558E-6	-210331.500023296	-60094.0000066561	300475.000033281
36	-2.97368408501804E-6	-235397.240020816	-67255.6400059474	336283.200029737
37	-2.66522957466352E-6	-262640.540018657	-75039.4400053305	375202.200026652
38	-2.39574209533138E-6	-292184.04001677	-83480.4400047915	417407.200023957
39	-2.15946248375913E-6	-324153.740015116	-92614.640004319	463078.200021595
40	-1.95160031217110E-6	-358679.000013661	-102479.000003903	512400.000019516

Answer 2

[Torsten]

Look whether this might help.

syms T
x = sym('x',[1 4]);
eqn1 = 10.*(T-x(1))+0.2.*(T.^4-x(1).^4) - x(4) == 0;
eqn2 = -1.*(1/x(1)-1/x(2)) - x(4) == 0;
eqn3 = 2.*(x(3)-x(2))-x(4) == 0;
eqn4 = 5.*(1-x(3))-x(4) == 0;
solve([eqn1,eqn2,eqn3,eqn4],x)

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

ans = struct with fields:
    x1: ((21*T^4)/100 + (21*T)/2 + 8)*root(z^9 - z^8*(10*T + T^4/5 + 40/7) + z^7*((400*T)/7 + (8*T^4)/7 + 390/49) - z^6*((8800*T)/49 + (176*T^4)/49 - 7200/343) + z^5*((124000*T)/343 + (2480*T^4)/343 - 273500/2401) - z^4*((1234000*T)/2401 + (24680*T^4)…
    x2: 1 - (7*root(z^9 - z^8*(10*T + T^4/5 + 40/7) + z^7*((400*T)/7 + (8*T^4)/7 + 390/49) - z^6*((8800*T)/49 + (176*T^4)/49 - 7200/343) + z^5*((124000*T)/343 + (2480*T^4)/343 - 273500/2401) - z^4*((1234000*T)/2401 + (24680*T^4)/2401 - 2987401/12005) …
    x3: 1 - root(z^9 - z^8*(10*T + T^4/5 + 40/7) + z^7*((400*T)/7 + (8*T^4)/7 + 390/49) - z^6*((8800*T)/49 + (176*T^4)/49 - 7200/343) + z^5*((124000*T)/343 + (2480*T^4)/343 - 273500/2401) - z^4*((1234000*T)/2401 + (24680*T^4)/2401 - 2987401/12005) + z…
    x4: root(z^9 - z^8*(10*T + T^4/5 + 40/7) + z^7*((400*T)/7 + (8*T^4)/7 + 390/49) - z^6*((8800*T)/49 + (176*T^4)/49 - 7200/343) + z^5*((124000*T)/343 + (2480*T^4)/343 - 273500/2401) - z^4*((1234000*T)/2401 + (24680*T^4)/2401 - 2987401/12005) + z^3*(…

It shows that x(1)-x(4) are related to the roots of a polynomial of degree 9 in T.