I have an equation that relies on previous values to get the next.
조회 수: 1 (최근 30일)
이전 댓글 표시
this is the basic set up i have
P=[1 2 3 4 5]
M1=0
P2/P1=(1+M2^2)/(1+M1^2)
i need to solve for M2, then using M2 as the new M1, like so
P3/P2=(1+M3^2)/(1+M2^2), solve for M3
reiterate that process till i have all values of M in a matrix anbd plot them.
댓글 수: 0
답변 (1개)
Star Strider
2022년 9월 28일
I am not certain how the ‘P’ vector enters into this. If:
P1 = P(1) = 1
P2 = P(2) = 2
P3 = P(3) = 3
in this instance, then:
P = [1 2 3 4 5];
P2P1 = @(M1,M2) (1+M2.^2)./(1+M1.^2) - P(2)./P(1);
P3P2 = @(M2,M3) (1+M3.^2)./(1+M2.^2) - P(3)./P(2);
Pfcn = @(M1,M2,M3) [P2P1(M1,M2); P3P2(M2,M3)]
format long
Pv = fsolve(@(b)Pfcn(b(1),b(2),b(3)), [0; 1; 1])
Make appropriate changes to get the result you want.
.
댓글 수: 5
Star Strider
2022년 9월 28일
So you are solving for parameter ‘M1’ as a function of ‘Po’. Is ‘t’ involved in this as a variable, or is it just there for reference?
M=((((Po2./(Po1.*(1+((2*gamma)./(gamma-1)).*((M1.^2)-1)))).^((gamma-1)/gamma)).*(1+((gamma-1)/2).*(M1.^2))-1).*(2/(gamma-1))).^(1/2)
Assuming that ‘Po1’ is ‘Po’ at time ‘t’ and ‘Po2’ is ‘Po’ at time ‘t+1’ —
t=[0.00
1.20
2.40
3.60
4.80
6.01
7.21
8.41
9.61
10.81
12.01
13.21
14.41
15.62
16.82
18.02
19.22
20.42
21.62
22.82
24.02
25.23
26.43
27.63
28.83
30.03
31.23
32.43
33.63
34.83
36.04
37.24
38.44
39.64
40.84
42.04
43.24
44.44
45.65
46.85
48.05
49.25
50.45
51.65
52.85
54.05
55.26
56.46
57.66
58.86
60.06
61.26
62.46
63.66
64.86
66.07
67.27
68.47
69.67
70.87
72.07
73.27
74.47
75.68
76.88
78.08
79.28
80.48
81.68
82.88
84.08
85.29
86.49
87.69
88.89
90.09
91.29
92.49
93.69
94.89
96.10
97.30
98.50
99.70
100.90
102.10
103.30
104.50
105.71
106.91
108.11
109.31
110.51
111.71
112.91
114.11
115.32
116.52
117.72
118.92
120.12
121.32
122.52
123.72
124.92
126.13
127.33
128.53
129.73
130.93
132.13
133.33
134.53
135.74
136.94
138.14
139.34
140.54
141.74
142.94
144.14
145.35
146.55
147.75
148.95
150.15
151.35
152.55
153.75
154.95
156.16
157.36
158.56
159.76
160.96
162.16
163.36
164.56
165.77
166.97
168.17
169.37
170.57
171.77
172.97
174.17
175.38
176.58
177.78
178.98
180.18
181.38
182.58
183.78
184.98
186.19
187.39
188.59
189.79
190.99
192.19
193.39
194.59
195.80
197.00
198.20
199.40
200.60
201.80
203.00
204.20
205.41
206.61
207.81
209.01
210.21
211.41
212.61
213.81
215.02
216.22
217.42
218.62
219.82
221.02
222.22
223.42
224.62
225.83
227.03
228.23
229.43
230.63
231.83
233.03
234.23
235.44
236.64
237.84
239.04
240.24
241.44
242.64
243.84
245.05
246.25
247.45
248.65
249.85
251.05
252.25
253.45
254.65
255.86
257.06
258.26
259.46
260.66
261.86
263.06
264.26
265.47
266.67
267.87
269.07
270.27
271.47
272.67
273.87
275.08
276.28
277.48
278.68
279.88
281.08
282.28
283.48
284.68
285.89
287.09
288.29
289.49
290.69
291.89
293.09
294.29
295.50
296.70
297.90
299.10
300.30
301.50
302.70
303.90
305.11
306.31
307.51
308.71
309.91
311.11
312.31
313.51
314.71
315.92
317.12
318.32
319.52
320.72
321.92
323.12
324.32
325.53
326.73
327.93
329.13
330.33
331.53
332.73
333.93
335.14
336.34
337.54
338.74
339.94
341.14
342.34
343.54
344.74
345.95
347.15
348.35
349.55
350.75
351.95
353.15
354.35
355.56
356.76
357.96
359.16
360.36
361.56
362.76
363.96
365.17
366.37
367.57
368.77
369.97
371.17
372.37
373.57
374.77
375.98
377.18
378.38
379.58
380.78
381.98
383.18
384.38
385.59
386.79
387.99
389.19
390.39
391.59
392.79
393.99
395.20
396.40
397.60
398.80
400.00
401.20
402.40
403.60
404.80
406.01
407.21
408.41
409.61
410.81
412.01
413.21
414.41
415.62
416.82
418.02
419.22
420.42
421.62
422.82
424.02
425.23
426.43
427.63
428.83
430.03
431.23
432.43
433.63
434.83
436.04
437.24
438.44
439.64
440.84
442.04
443.24
444.44
445.65
446.85
448.05
449.25
450.45
451.65
452.85
454.05
455.26
456.46
457.66
458.86
460.06
461.26
462.46
463.66
464.86
466.07
467.27
468.47
469.67
470.87
472.07
473.27
474.47
475.68
476.88
478.08
479.28
480.48
481.68
482.88
484.08
485.29
486.49
487.69
488.89
490.09
491.29
492.49
493.69
494.89
496.10
497.30
498.50
499.70
500.90
502.10
503.30
504.50
505.71
506.91
508.11
509.31
510.51
511.71
512.91
514.11
515.32
516.52
517.72
518.92
520.12
521.32
522.52
523.72
524.92
526.13
527.33
528.53
529.73
530.93
532.13
533.33
534.53
535.74
536.94
538.14
539.34
540.54
541.74
542.94
544.14
545.35
546.55
547.75
548.95
550.15
551.35
552.55
553.75
554.95
556.16
557.36
558.56
559.76
560.96
562.16
563.36
564.56
565.77
566.97
568.17
569.37
570.57
571.77
572.97
574.17
575.38
576.58
577.78
578.98
580.18
581.38
582.58
583.78
584.98
586.19
587.39
588.59
589.79
590.99
592.19
593.39
594.59
595.80
597.00
598.20
599.40
600.60
601.80
603.00
604.20
605.41
606.61
607.81
609.01
610.21
611.41
612.61
613.81
615.02
616.22
617.42
618.62
619.82
621.02
622.22
623.42
624.62
625.83
627.03
628.23
629.43
630.63
631.83
633.03
634.23
635.44
636.64
637.84
639.04
640.24
641.44
642.64
643.84
645.05
646.25
647.45
648.65
649.85
651.05
652.25
653.45
654.65
655.86
657.06
658.26
659.46
660.66
661.86
663.06
664.26
665.47
666.67
667.87
669.07
670.27
671.47
672.67
673.87
675.08
676.28
677.48
678.68
679.88
681.08
682.28
683.48
684.68
685.89
687.09
688.29
689.49
690.69
691.89
693.09
694.29
695.50
696.70
697.90
699.10
700.30
701.50
702.70
703.90
705.11
706.31
707.51
708.71
709.91
711.11
712.31
713.51
714.71
715.92
717.12
718.32
719.52
720.72
721.92
723.12
724.32
725.53
726.73
727.93
729.13
730.33
731.53
732.73
733.93
735.14
736.34
737.54
738.74
739.94
741.14
742.34
743.54
744.74
745.95
747.15
748.35
749.55
750.75
751.95
753.15
754.35
755.56
756.76
757.96
759.16
760.36
761.56
762.76
763.96
765.17
766.37
767.57
768.77
769.97
771.17
772.37
773.57
774.77
775.98
777.18
778.38
779.58
780.78
781.98
783.18
784.38
785.59
786.79
787.99
789.19
790.39
791.59
792.79
793.99
795.20
796.40
797.60
798.80
800.00
801.20
802.40
803.60
804.80
806.01
807.21
808.41
809.61
810.81
812.01
813.21
814.41
815.62
816.82
818.02
819.22
820.42
821.62
822.82
824.02
825.23
826.43
827.63
828.83
830.03
831.23
832.43
833.63
834.83
836.04
837.24
838.44
839.64
840.84
842.04
843.24
844.44
845.65
846.85
848.05
849.25
850.45
851.65
852.85
854.05
855.26
856.46
857.66
858.86
860.06
861.26
862.46
863.66
864.86
866.07
867.27
868.47
869.67
870.87
872.07
873.27
874.47
875.68
876.88
878.08
879.28
880.48
881.68
882.88
884.08
885.29
886.49
887.69
888.89
890.09
891.29
892.49
893.69
894.89
896.10
897.30
898.50
899.70
900.90
902.10
903.30
904.50
905.71
906.91
908.11
909.31
910.51
911.71
912.91
914.11
915.32
916.52
917.72
918.92
920.12
921.32
922.52
923.72
924.92
926.13
927.33
928.53
929.73
930.93
932.13
933.33
934.53
935.74
936.94
938.14
939.34
940.54
941.74
942.94
944.14
945.35
946.55
947.75
948.95
950.15
951.35
952.55
953.75
954.95
956.16
957.36
958.56
959.76
960.96
962.16
963.36
964.56
965.77
966.97
968.17
969.37
970.57
971.77
972.97
974.17
975.38
976.58
977.78
978.98
980.18
981.38
982.58
983.78
984.98
986.19
987.39
988.59
989.79
990.99
992.19
993.39
994.59
995.80
997.00
998.20
999.40
1000.60
1001.80
1003.00
1004.20
1005.41
1006.61
1007.81
1009.01
1010.21
1011.41
1012.61
1013.81
1015.02
1016.22
1017.42
1018.62
1019.82
1021.02
1022.22
1023.42
1024.62
1025.83
1027.03
1028.23
1029.43
1030.63
1031.83
1033.03
1034.23
1035.44
1036.64
1037.84
1039.04
1040.24
1041.44
1042.64
1043.84
1045.05
1046.25
1047.45
1048.65
1049.85
1051.05
1052.25
1053.45
1054.65
1055.86
1057.06
1058.26
1059.46
1060.66
1061.86
1063.06
1064.26
1065.47
1066.67
1067.87
1069.07
1070.27
1071.47
1072.67
1073.87
1075.08
1076.28
1077.48
1078.68
1079.88
1081.08
1082.28
1083.48
1084.68
1085.89
1087.09
1088.29
1089.49
1090.69
1091.89
1093.09
1094.29
1095.50
1096.70
1097.90
1099.10
1100.30
1101.50
1102.70
1103.90
1105.11
1106.31
1107.51
1108.71
1109.91
1111.11
1112.31
1113.51
1114.71
1115.92
1117.12
1118.32
1119.52
1120.72
1121.92
1123.12
1124.32
1125.53
1126.73
1127.93
1129.13
1130.33
1131.53
1132.73
1133.93
1135.14
1136.34
1137.54
1138.74
1139.94
1141.14
1142.34
1143.54
1144.74
1145.95
1147.15
1148.35
1149.55
1150.75
1151.95
1153.15
1154.35
1155.56
1156.76
1157.96
1159.16
1160.36
1161.56
1162.76
1163.96
1165.17
1166.37
1167.57
1168.77
1169.97
1171.17
1172.37
1173.57
1174.77
1175.98
1177.18
1178.38
1179.58
1180.78
1181.98
1183.18
1184.38
1185.59
1186.79
1187.99
1189.19
1190.39
1191.59
1192.79
1193.99
1195.20
1196.40
1197.60
1198.80
1200.00];%time t (s)
Po=[101034.72
100857.57
100680.46
100503.40
100326.37
100149.39
99972.45
99795.56
99618.71
99441.91
99265.16
99088.47
98911.82
98735.23
98558.70
98382.22
98205.80
98029.44
97853.15
97676.91
97500.75
97324.65
97148.62
96972.67
96796.78
96620.98
96445.25
96269.60
96094.03
95918.55
95743.15
95567.85
95392.63
95217.51
95042.48
94867.56
94692.74
94518.02
94343.41
94168.91
93994.52
93820.25
93646.09
93472.07
93298.16
93124.39
92950.74
92777.24
92603.87
92430.64
92257.56
92084.63
91911.86
91739.24
91566.79
91394.50
91222.38
91050.43
90878.67
90707.08
90535.69
90364.48
90193.48
90022.67
89852.07
89681.69
89511.52
89341.57
89171.85
89002.36
88833.11
88664.10
88495.35
88326.85
88158.61
87990.63
87822.94
87655.52
87488.39
87321.55
87155.01
86988.77
86822.86
86657.26
86491.99
86327.05
86162.46
85998.21
85834.33
85670.81
85507.66
85344.90
85182.53
85020.55
84858.99
84697.83
84537.11
84376.81
84216.96
84057.57
83898.63
83740.17
83582.19
83424.69
83267.71
83111.23
82955.27
82799.85
82644.97
82490.64
82336.88
82183.70
82031.11
81879.11
81727.73
81576.97
81426.85
81277.38
81128.56
80980.42
80832.97
80686.22
80540.18
80394.86
80250.29
80106.47
79963.42
79821.14
79679.67
79539.01
79399.17
79260.17
79122.03
78984.76
78848.38
78712.90
78578.34
78444.71
78312.04
78180.33
78049.61
77919.89
77791.19
77663.52
77536.91
77411.37
77286.92
77163.58
77041.36
76920.29
76800.39
76681.66
76564.15
76447.85
76332.79
76219.00
76106.49
75995.28
75885.39
75776.85
75669.67
75563.88
75459.49
75356.54
75255.03
75155.00
75056.47
74959.45
74863.97
74770.06
74677.74
74587.02
74497.94
74410.52
74324.78
74240.74
74158.44
74077.89
73999.13
73922.17
73847.04
73773.77
73702.38
73632.89
73565.35
73499.76
73436.17
73374.58
73315.04
73257.57
73202.20
73148.95
73097.85
73048.93
73002.23
72957.76
72915.55
72875.64
72838.06
72802.83
72769.98
72739.55
72711.56
72686.04
72663.02
72642.54
72624.63
72609.31
72596.62
72586.58
72579.24
72574.62
72572.75
72573.67
72577.40
72583.98
72593.45
72605.83
72621.16
72639.47
72660.80
72685.17
72712.62
72743.19
72776.91
72813.81
72853.92
72897.29
72943.94
72993.91
73047.24
73103.95
73164.08
73227.68
73294.77
73365.38
73439.56
73517.34
73598.75
73683.82
73772.61
73865.13
73961.42
74061.53
74165.48
74273.31
74385.06
74500.76
74620.44
74744.15
74871.92
75003.77
75139.76
75279.91
75424.25
75572.83
75725.67
75882.82
76044.30
76210.15
76380.40
76555.09
76734.25
76917.91
77106.12
77298.89
77496.26
77698.26
77904.93
78116.30
78332.39
78553.24
78778.87
79009.33
79244.63
79484.80
79729.87
79979.87
80234.83
80494.77
80759.72
81029.69
81304.72
81584.83
81870.04
82160.36
82455.83
82756.46
83062.27
83373.27
83689.49
84010.93
84337.62
84669.56
85006.77
85349.25
85697.02
86050.09
86408.45
86772.12
87141.10
87515.39
87894.99
88279.89
88670.10
89065.55
89466.02
89871.26
90281.04
90695.13
91113.30
91535.32
91960.96
92390.02
92822.27
93257.50
93695.50
94136.05
94578.95
95023.99
95470.98
95919.69
96369.95
96821.53
97274.26
97727.93
98182.34
98637.30
99092.62
99548.10
100003.56
100458.80
100913.63
101367.87
101821.32
102273.80
102725.13
103175.11
103623.56
104070.30
104515.14
104957.90
105398.40
105836.45
106271.88
106704.50
107134.13
107560.60
107983.72
108403.32
108819.22
109231.24
109639.20
110042.94
110442.28
110837.04
111227.06
111612.15
111992.15
112366.89
112736.20
113099.91
113457.85
113809.86
114155.78
114495.43
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101034.72]; %pressure (pa)
gamma=1.4;
M1fcn = @(M1,Po1,Po2) ((((Po2./(Po1.*(1+((2*gamma)./(gamma-1)).*((M1.^2)-1)))).^((gamma-1)/gamma)).*(1+((gamma-1)/2).*(M1.^2))-1).*(2/(gamma-1))).^(1/2);
for k = 1:numel(t)-1
M1(k) = fsolve(@(M1)M1fcn(M1,Po(k),Po(k+1)), 1E+2);
end
figure
% yyaxis left
plot(t(1:end-1), real(M1))
ylabel('Re[M1(t)]')
% yyaxis right
% plot(t(1:end-1), imag(M1))
% grid
xlabel('t')
% ylabel('Im[M1(t)]')
Does this seem to be correct? (I have no idea. Whatever you are doing is not an area of my expertise.) The imaginary parts of ‘M1’ are vanishingly small (2.5E-12 ± 3.5E-12) so they can be safely ignored.
.
Star Strider
2022년 9월 28일
I would like to help you with this.
I need you to describe step-by-step what you want to do.
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