Решение алгебраических и дифференциальных уравнений в пакете MatLab
Слово function в первой строке определяет, что данный файл содержит файл-функцию. Сохраняем этот файл с соответствующим именем fun. Далее в редакторе М-файлов пишем текст файл-программы: МИНИСТЕРСТВО ОБРАЗОВАНИЯ И НАУКИ РОССИЙСКОЙ ФЕДЕРАЦИИ Федеральное государственное автономное образовательное учреждение высшего профессионального образования. С использованием классических алгоритмов численных… Читать ещё >
Решение алгебраических и дифференциальных уравнений в пакете MatLab (реферат, курсовая, диплом, контрольная)
МИНИСТЕРСТВО ОБРАЗОВАНИЯ И НАУКИ РОССИЙСКОЙ ФЕДЕРАЦИИ Федеральное государственное автономное образовательное учреждение высшего профессионального образования.
«Дальневосточный федеральный университет».
ИНЖЕНЕРНАЯ ШКОЛА Кафедра электроэнергетики и электротехники КУРСОВАЯ РАБОТА.
«Решение алгебраических и дифференциальных уравнений в пакете MatLab».
Студент гр. Б-3205б Хомячук Артём Игоревич Руководитель доцент Н. М. Марченко г. Владивосток 2013.
1) Решение алгебраических уравнений..
1. (а) Задан один входной параметр:.
Файл-функции:.
function f1=fun (x).
f1=1.*cos (2.*x).*sin ((pi./3)+x);
Слово function в первой строке определяет, что данный файл содержит файл-функцию. Сохраняем этот файл с соответствующим именем fun. Далее в редакторе М-файлов пишем текст файл-программы:
Файл-программа:.
fprintf ('Таблица Значений Функции f1n');
fprintf ('——————————————n');
fprintf ('| x | y |n');
fprintf ('——————————————n');
x=[0:0.07:7];
y=fun (x);
v=[x, y];
fprintf ('| %6.2f | %6.2f |n', v).
plot (x, y,'m*-').
grid on.
hold on.
fplot ('fun',[0 7],'c-').
Результат работы программы:.
Таблица Значений Функции f1.
————————————-.
| x | y |.
—————————————.
| 0.00 | 0.07 |.
| 0.14 | 0.21 |.
| 0.28 | 0.35 |.
| 0.42 | 0.49 |.
| 0.56 | 0.63 |.
| 0.70 | 0.77 |.
| 0.84 | 0.91 |.
| 0.98 | 1.05 |.
| 1.12 | 1.19 |.
| 1.26 | 1.33 |.
| 1.40 | 1.47 |.
| 1.54 | 1.61 |.
| 1.68 | 1.75 |.
| 1.82 | 1.89 |.
| 1.96 | 2.03 |.
| 2.10 | 2.17 |.
| 2.24 | 2.31 |.
| 2.38 | 2.45 |.
| 2.52 | 2.59 |.
| 2.66 | 2.73 |.
| 2.80 | 2.87 |.
| 2.94 | 3.01 |.
| 3.08 | 3.15 |.
| 3.22 | 3.29 |.
| 3.36 | 3.43 |.
| 3.50 | 3.57 |.
| 3.64 | 3.71 |.
| 3.78 | 3.85 |.
| 3.92 | 3.99 |.
| 4.06 | 4.13 |.
| 4.20 | 4.27 |.
| 4.34 | 4.41 |.
| 4.48 | 4.55 |.
| 4.62 | 4.69 |.
| 4.76 | 4.83 |.
| 4.90 | 4.97 |.
| 5.04 | 5.11 |.
| 5.18 | 5.25 |.
| 5.32 | 5.39 |.
| 5.46 | 5.53 |.
| 5.60 | 5.67 |.
| 5.74 | 5.81 |.
| 5.88 | 5.95 |.
| 6.02 | 6.09 |.
| 6.16 | 6.23 |.
| 6.30 | 6.37 |.
| 6.44 | 6.51 |.
| 6.58 | 6.65 |.
| 6.72 | 6.79 |.
| 6.86 | 6.93 |.
| 7.00 | 0.87 |.
| 0.89 | 0.89 |.
| 0.87 | 0.82 |.
| 0.75 | 0.66 |.
| 0.56 | 0.44 |.
| 0.30 | 0.17 |.
| 0.03 | -0.10 |.
| -0.23 | -0.34 |.
| -0.44 | -0.51 |.
| -0.57 | -0.60 |.
| -0.61 | -0.60 |.
| -0.57 | -0.53 |.
| -0.46 | -0.39 |.
| -0.32 | -0.24 |.
| -0.16 | -0.10 |.
| -0.04 | 0.00 |.
| 0.03 | 0.03 |.
| 0.02 | -0.01 |.
| -0.06 | -0.13 |.
| -0.21 | -0.31 |.
| -0.40 | -0.50 |.
| -0.60 | -0.69 |.
| -0.77 | -0.83 |.
| -0.87 | -0.89 |.
| -0.89 | -0.86 |.
| -0.82 | -0.74 |.
| -0.65 | -0.54 |.
| -0.42 | -0.29 |.
| -0.15 | -0.01 |.
| 0.12 | 0.24 |.
| 0.35 | 0.45 |.
| 0.52 | 0.57 |.
| 0.60 | 0.61 |.
| 0.60 | 0.57 |.
| 0.52 | 0.46 |.
| 0.38 | 0.31 |.
| 0.23 | 0.15 |.
| 0.09 | 0.03 |.
| -0.01 | -0.03 |.
| -0.03 | -0.02 |.
| 0.02 | 0.07 |.
| 0.14 | 0.22 |.
| 0.32 | 0.42 |.
| 0.51 | 0.61 |.
| 0.70 | 0.77 |.
| 0.83 | 0.87 |.
| 0.89 | 0.89 |.
| 0.86 | 0.81 |.
| 0.73 | 0.64 |.
| 0.53 | 0.40 |.
| 0.27 | 0.13 |.
2. (б) Задано несколько входных параметров:.
Файл-функция:.
дифференциальный уравнение эйлер программа.
function r=rad (x, y, z).
r=((x4)+5*(y2)+21*z)/(sqrt ((x3)+1));
Файл-программа:.
r=rad (1,2,3).
Результат работы программы: r = 59.3970.
3. (в) Задано несколько выходных аргументов:.
Файл-функция:.
function [f3,f4,f5]=mad (x).
f3=2*sin (3*x)+3*cos (2*x);
f4=(sqrt (x+1)+2*x)/((x2)+1);
f5=-4*(x^(-2));
Файл-программа:.
x=7;
[f3,f4,f5]=mad (x).
Результат работы программы:.
f3 = 2.0835.
f4 = 0.3366.
f5 = -0.0816.
Решение дифференциальных уравнений.
,.
а) с использованием классических алгоритмов численных методов Эйлера и Рунге-Кутта4-го порядка; Метод Эйлера:.
Алгоритм решения дифференциального уравнения методом Эйлера.
Файл-функция:.
function f=fun (x).
f=x;
Файл-программа:.
t0=0;
tk=5;
h=0.05;
a=5;
b=10;
y=0;
fprintf ('Таблица значений по МЭn');
fprintf ('…n');
fprintf ('| t | x | y |n');
fprintf ('…n');
for t=t0:h:tk.
x=(a/b)*sqrt (t);
f=faaan (x);
y=y+h*f;
fprintf ('| %4.2f | %4.4f | %4.4f |n', t, x, y);
plot (t, x,'r+').
grid on.
hold on.
plot (t, y,'b*').
xlabel ('t');
ylabel ('y');
end.
Результат работы программы:.
Таблица значений по МЭ.
….
| t | x | y _ |.
….
| 0.00 | 0.0000 | 0.0000 |.
| 0.01 | 0.0500 | 0.0005 |.
| 0.02 | 0.0707 | 0.0012 |.
| 0.03 | 0.0866 | 0.0021 |.
| 0.04 | 0.1000 | 0.0031 |.
| 0.05 | 0.1118 | 0.0042 |.
| 0.06 | 0.1225 | 0.0054 |.
| 0.07 | 0.1323 | 0.0067 |.
| 0.08 | 0.1414 | 0.0082 |.
| 0.09 | 0.1500 | 0.0097 |.
| 0.10 | 0.1581 | 0.0112 |.
| 0.11 | 0.1658 | 0.0129 |.
| 0.12 | 0.1732 | 0.0146 |.
| 0.13 | 0.1803 | 0.0164 |.
| 0.14 | 0.1871 | 0.0183 |.
| 0.15 | 0.1936 | 0.0202 |.
| 0.16 | 0.2000 | 0.0222 |.
| 0.17 | 0.2062 | 0.0243 |.
| 0.18 | 0.2121 | 0.0264 |.
| 0.19 | 0.2179 | 0.0286 |.
| 0.20 | 0.2236 | 0.0308 |.
| 0.21 | 0.2291 | 0.0331 |.
| 0.22 | 0.2345 | 0.0355 |.
| 0.23 | 0.2398 | 0.0379 |.
| 0.24 | 0.2449 | 0.0403 |.
| 0.25 | 0.2500 | 0.0428 |.
| 0.26 | 0.2550 | 0.0454 |.
| 0.27 | 0.2598 | 0.0480 |.
| 0.28 | 0.2646 | 0.0506 |.
| 0.29 | 0.2693 | 0.0533 |.
| 0.30 | 0.2739 | 0.0560 |.
| 0.31 | 0.2784 | 0.0588 |.
| 0.32 | 0.2828 | 0.0617 |.
| 0.33 | 0.2872 | 0.0645 |.
| 0.34 | 0.2915 | 0.0674 |.
| 0.35 | 0.2958 | 0.0704 |.
| 0.36 | 0.3000 | 0.0734 |.
| 0.37 | 0.3041 | 0.0764 |.
| 0.38 | 0.3082 | 0.0795 |.
| 0.39 | 0.3122 | 0.0826 |.
| 0.40 | 0.3162 | 0.0858 |.
| 0.41 | 0.3202 | 0.0890 |.
| 0.42 | 0.3240 | 0.0922 |.
| 0.43 | 0.3279 | 0.0955 |.
| 0.44 | 0.3317 | 0.0988 |.
| 0.45 | 0.3354 | 0.1022 |.
| 0.46 | 0.3391 | 0.1056 |.
| 0.47 | 0.3428 | 0.1090 |.
| 0.48 | 0.3464 | 0.1125 |.
| 0.49 | 0.3500 | 0.1160 |.
| 0.50 | 0.3536 | 0.1195 |.
| 0.51 | 0.3571 | 0.1231 |.
| 0.52 | 0.3606 | 0.1267 |.
| 0.53 | 0.3640 | 0.1303 |.
| 0.54 | 0.3674 | 0.1340 |.
| 0.55 | 0.3708 | 0.1377 |.
| 0.56 | 0.3742 | 0.1415 |.
| 0.57 | 0.3775 | 0.1452 |.
| 0.58 | 0.3808 | 0.1490 |.
| 0.59 | 0.3841 | 0.1529 |.
| 0.60 | 0.3873 | 0.1568 |.
| 0.61 | 0.3905 | 0.1607 |.
| 0.62 | 0.3937 | 0.1646 |.
| 0.63 | 0.3969 | 0.1686 |.
| 0.64 | 0.4000 | 0.1726 |.
| 0.65 | 0.4031 | 0.1766 |.
| 0.66 | 0.4062 | 0.1807 |.
| 0.67 | 0.4093 | 0.1848 |.
| 0.68 | 0.4123 | 0.1889 |.
| 0.69 | 0.4153 | 0.1930 |.
| 0.70 | 0.4183 | 0.1972 |.
| 0.71 | 0.4213 | 0.2014 |.
| 0.72 | 0.4243 | 0.2057 |.
| 0.73 | 0.4272 | 0.2099 |.
| 0.74 | 0.4301 | 0.2142 |.
| 0.75 | 0.4330 | 0.2186 |.
| 0.76 | 0.4359 | 0.2229 |.
| 0.77 | 0.4387 | 0.2273 |.
| 0.78 | 0.4416 | 0.2317 |.
| 0.79 | 0.4444 | 0.2362 |.
| 0.80 | 0.4472 | 0.2406 |.
| 0.81 | 0.4500 | 0.2451 |.
| 0.82 | 0.4528 | 0.2497 |.
| 0.83 | 0.4555 | 0.2542 |.
| 0.84 | 0.4583 | 0.2588 |.
| 0.85 | 0.4610 | 0.2634 |.
| 0.86 | 0.4637 | 0.2681 |.
| 0.87 | 0.4664 | 0.2727 |.
| 0.88 | 0.4690 | 0.2774 |.
| 0.89 | 0.4717 | 0.2821 |.
| 0.90 | 0.4743 | 0.2869 |.
| 0.91 | 0.4770 | 0.2916 |.
| 0.92 | 0.4796 | 0.2964 |.
| 0.93 | 0.4822 | 0.3013 |.
| 0.94 | 0.4848 | 0.3061 |.
| 0.95 | 0.4873 | 0.3110 |.
| 0.96 | 0.4899 | 0.3159 |.
| 0.97 | 0.4924 | 0.3208 |.
| 0.98 | 0.4950 | 0.3258 |.
| 0.99 | 0.4975 | 0.3307 |.
| 1.00 | 0.5000 | 0.3357 |.
| 1.01 | 0.5025 | 0.3408 |.
| 1.02 | 0.5050 | 0.3458 |.
| 1.03 | 0.5074 | 0.3509 |.
| 1.04 | 0.5099 | 0.3560 |.
| 1.05 | 0.5123 | 0.3611 |.
| 1.06 | 0.5148 | 0.3663 |.
| 1.07 | 0.5172 | 0.3714 |.
| 1.08 | 0.5196 | 0.3766 |.
| 1.09 | 0.5220 | 0.3818 |.
| 1.10 | 0.5244 | 0.3871 |.
| 1.11 | 0.5268 | 0.3924 |.
| 1.12 | 0.5292 | 0.3976 |.
| 1.13 | 0.5315 | 0.4030 |.
| 1.14 | 0.5339 | 0.4083 |.
| 1.15 | 0.5362 | 0.4137 |.
| 1.16 | 0.5385 | 0.4190 |.
| 1.17 | 0.5408 | 0.4245 |.
| 1.18 | 0.5431 | 0.4299 |.
| 1.19 | 0.5454 | 0.4353 |.
| 1.20 | 0.5477 | 0.4408 |.
| 1.21 | 0.5500 | 0.4463 |.
| 1.22 | 0.5523 | 0.4518 |.
| 1.23 | 0.5545 | 0.4574 |.
| 1.24 | 0.5568 | 0.4630 |.
| 1.25 | 0.5590 | 0.4685 |.
| 1.26 | 0.5612 | 0.4742 |.
| 1.27 | 0.5635 | 0.4798 |.
| 1.28 | 0.5657 | 0.4854 |.
| 1.29 | 0.5679 | 0.4911 |.
| 1.30 | 0.5701 | 0.4968 |.
| 1.31 | 0.5723 | 0.5025 |.
| 1.32 | 0.5745 | 0.5083 |.
| 1.33 | 0.5766 | 0.5141 |.
| 1.34 | 0.5788 | 0.5198 |.
| 1.35 | 0.5809 | 0.5257 |.
| 1.36 | 0.5831 | 0.5315 |.
| 1.37 | 0.5852 | 0.5373 |.
| 1.38 | 0.5874 | 0.5432 |.
| 1.39 | 0.5895 | 0.5491 |.
| 1.40 | 0.5916 | 0.5550 |.
| 1.41 | 0.5937 | 0.5610 |.
| 1.42 | 0.5958 | 0.5669 |.
| 1.43 | 0.5979 | 0.5729 |.
| 1.44 | 0.6000 | 0.5789 |.
| 1.45 | 0.6021 | 0.5849 |.
| 1.46 | 0.6042 | 0.5910 |.
| 1.47 | 0.6062 | 0.5970 |.
| 1.48 | 0.6083 | 0.6031 |.
| 1.49 | 0.6103 | 0.6092 |.
| 1.50 | 0.6124 | 0.6153 |.
| 1.51 | 0.6144 | 0.6215 |.
| 1.52 | 0.6164 | 0.6276 |.
| 1.53 | 0.6185 | 0.6338 |.
| 1.54 | 0.6205 | 0.6400 |.
| 1.55 | 0.6225 | 0.6463 |.
| 1.56 | 0.6245 | 0.6525 |.
| 1.57 | 0.6265 | 0.6588 |.
| 1.58 | 0.6285 | 0.6650 |.
| 1.59 | 0.6305 | 0.6714 |.
| 1.60 | 0.6325 | 0.6777 |.
| 1.61 | 0.6344 | 0.6840 |.
| 1.62 | 0.6364 | 0.6904 |.
| 1.63 | 0.6384 | 0.6968 |.
| 1.64 | 0.6403 | 0.7032 |.
| 1.65 | 0.6423 | 0.7096 |.
| 1.66 | 0.6442 | 0.7160 |.
| 1.67 | 0.6461 | 0.7225 |.
| 1.68 | 0.6481 | 0.7290 |.
| 1.69 | 0.6500 | 0.7355 |.
| 1.70 | 0.6519 | 0.7420 |.
| 1.71 | 0.6538 | 0.7485 |.
| 1.72 | 0.6557 | 0.7551 |.
| 1.73 | 0.6576 | 0.7617 |.
| 1.74 | 0.6595 | 0.7683 |.
| 1.75 | 0.6614 | 0.7749 |.
| 1.76 | 0.6633 | 0.7815 |.
| 1.77 | 0.6652 | 0.7882 |.
| 1.78 | 0.6671 | 0.7948 |.
| 1.79 | 0.6690 | 0.8015 |.
| 1.80 | 0.6708 | 0.8082 |.
| 1.81 | 0.6727 | 0.8150 |.
| 1.82 | 0.6745 | 0.8217 |.
| 1.83 | 0.6764 | 0.8285 |.
| 1.84 | 0.6782 | 0.8353 |.
| 1.85 | 0.6801 | 0.8421 |.
| 1.86 | 0.6819 | 0.8489 |.
| 1.87 | 0.6837 | 0.8557 |.
| 1.88 | 0.6856 | 0.8626 |.
| 1.89 | 0.6874 | 0.8694 |.
| 1.90 | 0.6892 | 0.8763 |.
| 1.91 | 0.6910 | 0.8832 |.
| 1.92 | 0.6928 | 0.8902 |.
| 1.93 | 0.6946 | 0.8971 |.
| 1.94 | 0.6964 | 0.9041 |.
| 1.95 | 0.6982 | 0.9111 |.
| 1.96 | 0.7000 | 0.9181 |.
| 1.97 | 0.7018 | 0.9251 |.
| 1.98 | 0.7036 | 0.9321 |.
| 1.99 | 0.7053 | 0.9392 |.
| 2.00 | 0.7071 | 0.9462 |.
| 2.01 | 0.7089 | 0.9533 |.
| 2.02 | 0.7106 | 0.9604 |.
| 2.03 | 0.7124 | 0.9676 |.
| 2.04 | 0.7141 | 0.9747 |.
| 2.05 | 0.7159 | 0.9819 |.
| 2.06 | 0.7176 | 0.9890 |.
| 2.07 | 0.7194 | 0.9962 |.
| 2.08 | 0.7211 | 1.0034 |.
| 2.09 | 0.7228 | 1.0107 |.
| 2.10 | 0.7246 | 1.0179 |.
| 2.11 | 0.7263 | 1.0252 |.
| 2.12 | 0.7280 | 1.0325 |.
| 2.13 | 0.7297 | 1.0398 |.
| 2.14 | 0.7314 | 1.0471 |.
| 2.15 | 0.7331 | 1.0544 |.
| 2.16 | 0.7348 | 1.0618 |.
| 2.17 | 0.7365 | 1.0691 |.
| 2.18 | 0.7382 | 1.0765 |.
| 2.19 | 0.7399 | 1.0839 |.
| 2.20 | 0.7416 | 1.0913 |.
| 2.21 | 0.7433 | 1.0987 |.
| 2.22 | 0.7450 | 1.1062 |.
| 2.23 | 0.7467 | 1.1137 |.
| 2.24 | 0.7483 | 1.1211 |.
| 2.25 | 0.7500 | 1.1286 |.
| 2.26 | 0.7517 | 1.1362 |.
| 2.27 | 0.7533 | 1.1437 |.
| 2.28 | 0.7550 | 1.1512 |.
| 2.29 | 0.7566 | 1.1588 |.
| 2.30 | 0.7583 | 1.1664 |.
| 2.31 | 0.7599 | 1.1740 |.
| 2.32 | 0.7616 | 1.1816 |.
| 2.33 | 0.7632 | 1.1892 |.
| 2.34 | 0.7649 | 1.1969 |.
| 2.35 | 0.7665 | 1.2046 |.
| 2.36 | 0.7681 | 1.2122 |.
| 2.37 | 0.7697 | 1.2199 |.
| 2.38 | 0.7714 | 1.2276 |.
| 2.39 | 0.7730 | 1.2354 |.
| 2.40 | 0.7746 | 1.2431 |.
| 2.41 | 0.7762 | 1.2509 |.
| 2.42 | 0.7778 | 1.2587 |.
| 2.43 | 0.7794 | 1.2665 |.
| 2.44 | 0.7810 | 1.2743 |.
| 2.45 | 0.7826 | 1.2821 |.
| 2.46 | 0.7842 | 1.2899 |.
| 2.47 | 0.7858 | 1.2978 |.
| 2.48 | 0.7874 | 1.3057 |.
| 2.49 | 0.7890 | 1.3136 |.
| 2.50 | 0.7906 | 1.3215 |.
| 2.51 | 0.7921 | 1.3294 |.
| 2.52 | 0.7937 | 1.3373 |.
| 2.53 | 0.7953 | 1.3453 |.
| 2.54 | 0.7969 | 1.3532 |.
| 2.55 | 0.7984 | 1.3612 |.
| 2.56 | 0.8000 | 1.3692 |.
| 2.57 | 0.8016 | 1.3772 |.
| 2.58 | 0.8031 | 1.3853 |.
| 2.59 | 0.8047 | 1.3933 |.
| 2.60 | 0.8062 | 1.4014 |.
| 2.61 | 0.8078 | 1.4095 |.
| 2.62 | 0.8093 | 1.4176 |.
| 2.63 | 0.8109 | 1.4257 |.
| 2.64 | 0.8124 | 1.4338 |.
| 2.65 | 0.8139 | 1.4419 |.
| 2.66 | 0.8155 | 1.4501 |.
| 2.67 | 0.8170 | 1.4583 |.
| 2.68 | 0.8185 | 1.4664 |.
| 2.69 | 0.8201 | 1.4746 |.
| 2.70 | 0.8216 | 1.4829 |.
| 2.71 | 0.8231 | 1.4911 |.
| 2.72 | 0.8246 | 1.4993 |.
| 2.73 | 0.8261 | 1.5076 |.
| 2.74 | 0.8276 | 1.5159 |.
| 2.75 | 0.8292 | 1.5242 |.
| 2.76 | 0.8307 | 1.5325 |.
| 2.77 | 0.8322 | 1.5408 |.
| 2.78 | 0.8337 | 1.5491 |.
| 2.79 | 0.8352 | 1.5575 |.
| 2.80 | 0.8367 | 1.5658 |.
| 2.81 | 0.8382 | 1.5742 |.
| 2.82 | 0.8396 | 1.5826 |.
| 2.83 | 0.8411 | 1.5910 |.
| 2.84 | 0.8426 | 1.5995 |.
| 2.85 | 0.8441 | 1.6079 |.
| 2.86 | 0.8456 | 1.6164 |.
| 2.87 | 0.8471 | 1.6248 |.
| 2.88 | 0.8485 | 1.6333 |.
| 2.89 | 0.8500 | 1.6418 |.
| 2.90 | 0.8515 | 1.6503 |.
| 2.91 | 0.8529 | 1.6589 |.
| 2.92 | 0.8544 | 1.6674 |.
| 2.93 | 0.8559 | 1.6760 |.
| 2.94 | 0.8573 | 1.6845 |.
| 2.95 | 0.8588 | 1.6931 |.
| 2.96 | 0.8602 | 1.7017 |.
| 2.97 | 0.8617 | 1.7103 |.
| 2.98 | 0.8631 | 1.7190 |.
| 2.99 | 0.8646 | 1.7276 |.
| 3.00 | 0.8660 | 1.7363 |.
| 3.01 | 0.8675 | 1.7450 |.
| 3.02 | 0.8689 | 1.7536 |.
| 3.03 | 0.8703 | 1.7623 |.
| 3.04 | 0.8718 | 1.7711 |.
| 3.05 | 0.8732 | 1.7798 |.
| 3.06 | 0.8746 | 1.7885 |.
| 3.07 | 0.8761 | 1.7973 |.
| 3.08 | 0.8775 | 1.8061 |.
| 3.09 | 0.8789 | 1.8149 |.
| 3.10 | 0.8803 | 1.8237 |.
| 3.11 | 0.8818 | 1.8325 |.
| 3.12 | 0.8832 | 1.8413 |.
| 3.13 | 0.8846 | 1.8502 |.
| 3.14 | 0.8860 | 1.8590 |.
| 3.15 | 0.8874 | 1.8679 |.
| 3.16 | 0.8888 | 1.8768 |.
| 3.17 | 0.8902 | 1.8857 |.
| 3.18 | 0.8916 | 1.8946 |.
| 3.19 | 0.8930 | 1.9035 |.
| 3.20 | 0.8944 | 1.9125 |.
| 3.21 | 0.8958 | 1.9214 |.
| 3.22 | 0.8972 | 1.9304 |.
| 3.23 | 0.8986 | 1.9394 |.
| 3.24 | 0.9000 | 1.9484 |.
| 3.25 | 0.9014 | 1.9574 |.
| 3.26 | 0.9028 | 1.9664 |.
| 3.27 | 0.9042 | 1.9755 |.
| 3.28 | 0.9055 | 1.9845 |.
| 3.29 | 0.9069 | 1.9936 |.
| 3.30 | 0.9083 | 2.0027 |.
| 3.31 | 0.9097 | 2.0118 |.
| 3.32 | 0.9110 | 2.0209 |.
| 3.33 | 0.9124 | 2.0300 |.
| 3.34 | 0.9138 | 2.0392 |.
| 3.35 | 0.9152 | 2.0483 |.
| 3.36 | 0.9165 | 2.0575 |.
| 3.37 | 0.9179 | 2.0667 |.
| 3.38 | 0.9192 | 2.0758 |.
| 3.39 | 0.9206 | 2.0851 |.
| 3.40 | 0.9220 | 2.0943 |.
| 3.41 | 0.9233 | 2.1035 |.
| 3.42 | 0.9247 | 2.1128 |.
| 3.43 | 0.9260 | 2.1220 |.
| 3.44 | 0.9274 | 2.1313 |.
| 3.45 | 0.9287 | 2.1406 |.
| 3.46 | 0.9301 | 2.1499 |.
| 3.47 | 0.9314 | 2.1592 |.
| 3.48 | 0.9327 | 2.1685 |.
| 3.49 | 0.9341 | 2.1779 |.
| 3.50 | 0.9354 | 2.1872 |.
| 3.51 | 0.9367 | 2.1966 |.
| 3.52 | 0.9381 | 2.2060 |.
| 3.53 | 0.9394 | 2.2154 |.
| 3.54 | 0.9407 | 2.2248 |.
| 3.55 | 0.9421 | 2.2342 |.
| 3.56 | 0.9434 | 2.2436 |.
| 3.57 | 0.9447 | 2.2531 |.
| 3.58 | 0.9460 | 2.2625 |.
| 3.59 | 0.9474 | 2.2720 |.
| 3.60 | 0.9487 | 2.2815 |.
| 3.61 | 0.9500 | 2.2910 |.
| 3.62 | 0.9513 | 2.3005 |.
| 3.63 | 0.9526 | 2.3100 |.
| 3.64 | 0.9539 | 2.3196 |.
| 3.65 | 0.9552 | 2.3291 |.
| 3.66 | 0.9566 | 2.3387 |.
| 3.67 | 0.9579 | 2.3483 |.
| 3.68 | 0.9592 | 2.3578 |.
| 3.69 | 0.9605 | 2.3675 |.
| 3.70 | 0.9618 | 2.3771 |.
| 3.71 | 0.9631 | 2.3867 |.
| 3.72 | 0.9644 | 2.3963 |.
| 3.73 | 0.9657 | 2.4060 |.
| 3.74 | 0.9670 | 2.4157 |.
| 3.75 | 0.9682 | 2.4254 |.
| 3.76 | 0.9695 | 2.4350 |.
| 3.77 | 0.9708 | 2.4448 |.
| 3.78 | 0.9721 | 2.4545 |.
| 3.79 | 0.9734 | 2.4642 |.
| 3.80 | 0.9747 | 2.4740 |.
| 3.81 | 0.9760 | 2.4837 |.
| 3.82 | 0.9772 | 2.4935 |.
| 3.83 | 0.9785 | 2.5033 |.
| 3.84 | 0.9798 | 2.5131 |.
| 3.85 | 0.9811 | 2.5229 |.
| 3.86 | 0.9823 | 2.5327 |.
| 3.87 | 0.9836 | 2.5425 |.
| 3.88 | 0.9849 | 2.5524 |.
| 3.89 | 0.9862 | 2.5623 |.
| 3.90 | 0.9874 | 2.5721 |.
| 3.91 | 0.9887 | 2.5820 |.
| 3.92 | 0.9899 | 2.5919 |.
| 3.93 | 0.9912 | 2.6018 |.
| 3.94 | 0.9925 | 2.6118 |.
| 3.95 | 0.9937 | 2.6217 |.
| 3.96 | 0.9950 | 2.6316 |.
| 3.97 | 0.9962 | 2.6416 |.
| 3.98 | 0.9975 | 2.6516 |.
| 3.99 | 0.9987 | 2.6616 |.
| 4.00 | 1.0000 | 2.6716 |.
| 4.01 | 1.0012 | 2.6816 |.
| 4.02 | 1.0025 | 2.6916 |.
| 4.03 | 1.0037 | 2.7016 |.
| 4.04 | 1.0050 | 2.7117 |.
| 4.05 | 1.0062 | 2.7218 |.
| 4.06 | 1.0075 | 2.7318 |.
| 4.07 | 1.0087 | 2.7419 |.
| 4.08 | 1.0100 | 2.7520 |.
| 4.09 | 1.0112 | 2.7621 |.
| 4.10 | 1.0124 | 2.7722 |.
| 4.11 | 1.0137 | 2.7824 |.
| 4.12 | 1.0149 | 2.7925 |.
| 4.13 | 1.0161 | 2.8027 |.
| 4.14 | 1.0173 | 2.8129 |.
| 4.15 | 1.0186 | 2.8231 |.
| 4.16 | 1.0198 | 2.8333 |.
| 4.17 | 1.0210 | 2.8435 |.
| 4.18 | 1.0223 | 2.8537 |.
| 4.19 | 1.0235 | 2.8639 |.
| 4.20 | 1.0247 | 2.8742 |.
| 4.21 | 1.0259 | 2.8844 |.
| 4.22 | 1.0271 | 2.8947 |.
| 4.23 | 1.0283 | 2.9050 |.
| 4.24 | 1.0296 | 2.9153 |.
| 4.25 | 1.0308 | 2.9256 |.
| 4.26 | 1.0320 | 2.9359 |.
| 4.27 | 1.0332 | 2.9462 |.
| 4.28 | 1.0344 | 2.9566 |.
| 4.29 | 1.0356 | 2.9669 |.
| 4.30 | 1.0368 | 2.9773 |.
| 4.31 | 1.0380 | 2.9877 |.
| 4.32 | 1.0392 | 2.9981 |.
| 4.33 | 1.0404 | 3.0085 |.
| 4.34 | 1.0416 | 3.0189 |.
| 4.35 | 1.0428 | 3.0293 |.
| 4.36 | 1.0440 | 3.0398 |.
| 4.37 | 1.0452 | 3.0502 |.
| 4.38 | 1.0464 | 3.0607 |.
| 4.39 | 1.0476 | 3.0712 |.
| 4.40 | 1.0488 | 3.0816 |.
| 4.41 | 1.0500 | 3.0921 |.
| 4.42 | 1.0512 | 3.1027 |.
| 4.43 | 1.0524 | 3.1132 |.
| 4.44 | 1.0536 | 3.1237 |.
| 4.45 | 1.0548 | 3.1343 |.
| 4.46 | 1.0559 | 3.1448 |.
| 4.47 | 1.0571 | 3.1554 |.
| 4.48 | 1.0583 | 3.1660 |.
| 4.49 | 1.0595 | 3.1766 |.
| 4.50 | 1.0607 | 3.1872 |.
| 4.51 | 1.0618 | 3.1978 |.
| 4.52 | 1.0630 | 3.2084 |.
| 4.53 | 1.0642 | 3.2191 |.
| 4.54 | 1.0654 | 3.2297 |.
| 4.55 | 1.0665 | 3.2404 |.
| 4.56 | 1.0677 | 3.2511 |.
| 4.57 | 1.0689 | 3.2618 |.
| 4.58 | 1.0700 | 3.2725 |.
| 4.59 | 1.0712 | 3.2832 |.
| 4.60 | 1.0724 | 3.2939 |.
| 4.61 | 1.0735 | 3.3046 |.
| 4.62 | 1.0747 | 3.3154 |.
| 4.63 | 1.0759 | 3.3261 |.
| 4.64 | 1.0770 | 3.3369 |.
| 4.65 | 1.0782 | 3.3477 |.
| 4.66 | 1.0794 | 3.3585 |.
| 4.67 | 1.0805 | 3.3693 |.
| 4.68 | 1.0817 | 3.3801 |.
| 4.69 | 1.0828 | 3.3909 |.
| 4.70 | 1.0840 | 3.4018 |.
| 4.71 | 1.0851 | 3.4126 |.
| 4.72 | 1.0863 | 3.4235 |.
| 4.73 | 1.0874 | 3.4344 |.
| 4.74 | 1.0886 | 3.4452 |.
| 4.75 | 1.0897 | 3.4561 |.
| 4.76 | 1.0909 | 3.4670 |.
| 4.77 | 1.0920 | 3.4780 |.
| 4.78 | 1.0932 | 3.4889 |.
| 4.79 | 1.0943 | 3.4998 |.
| 4.80 | 1.0954 | 3.5108 |.
| 4.81 | 1.0966 | 3.5218 |.
| 4.82 | 1.0977 | 3.5327 |.
| 4.83 | 1.0989 | 3.5437 |.
| 4.84 | 1.1000 | 3.5547 |.
| 4.85 | 1.1011 | 3.5657 |.
| 4.86 | 1.1023 | 3.5768 |.
| 4.87 | 1.1034 | 3.5878 |.
| 4.88 | 1.1045 | 3.5988 |.
| 4.89 | 1.1057 | 3.6099 |.
| 4.90 | 1.1068 | 3.6210 |.
| 4.91 | 1.1079 | 3.6320 |.
| 4.92 | 1.1091 | 3.6431 |.
| 4.93 | 1.1102 | 3.6542 |.
| 4.94 | 1.1113 | 3.6654 |.
| 4.95 | 1.1124 | 3.6765 |.
| 4.96 | 1.1136 | 3.6876 |.
| 4.97 | 1.1147 | 3.6988 |.
| 4.98 | 1.1158 | 3.7099 |.
| 4.99 | 1.1169 | 3.7211 |.
| 5.00 | 1.1180 | 3.7323 |.
Метод Рунге-Кутта 4-го порядка:.
Алгоритм решения дифференциального уравнения.
методом Рунге-Кутта 4-го порядка..
Файл-функция:.
function f=faaan (x).
f=x;
Файл-программа:.
a=5;
b=10;
h=0.05;
t0=0;
tk=5;
y=0;
y1=0;
fprintf ('Таблица значений по МРГn');
fprintf ('—————————————n');
fprintf ('| t | x | y |n');
fprintf ('—————————————n');
t=t0;
x=(a/b)*sqrt (t);
fprintf ('| %4.2f | %4.4f | %4.4f |n', t, x, y);
while t.
f=faaan (x);
k=h*f;
s=k;
y=y+k/2;
t=t+h/2;
x=(a/b)*sqrt (t);
for j=1:2.
f=faaan (x);
k=h*f;
s=s+2*k;
y=y1+k/2;
end.
t=t+h/2;
x=(a/b)*sqrt (t);
y=y+k/2;
f=faaan (x);
k=h*f;
s=s+k;
y=y1+s/6;
fprintf ('| %4.2f | %4.4f | %4.4f |n', t, x, y);
plot (t, x,'r*').
grid on.
hold on.
plot (t, y,'k+').
xlabel ('t');
ylabel ('y');
y1=y;
end.
Результат работы программы:.
Таблица значений по МРГ.
———————————————.
| t | x | y |.
———————————————.
| 0.00 | 0.0000 | 0.0000 |.
| 0.05 | 0.1118 | 0.0036 |.
| 0.10 | 0.1581 | 0.0104 |.
| 0.15 | 0.1936 | 0.0192 |.
| 0.20 | 0.2236 | 0.0297 |.
| 0.25 | 0.2500 | 0.0415 |.
| 0.30 | 0.2739 | 0.0546 |.
| 0.35 | 0.2958 | 0.0689 |.
| 0.40 | 0.3162 | 0.0842 |.
| 0.45 | 0.3354 | 0.1005 |.
| 0.50 | 0.3536 | 0.1177 |.
| 0.55 | 0.3708 | 0.1358 |.
| 0.60 | 0.3873 | 0.1548 |.
| 0.65 | 0.4031 | 0.1745 |.
| 0.70 | 0.4183 | 0.1951 |.
| 0.75 | 0.4330 | 0.2163 |.
| 0.80 | 0.4472 | 0.2384 |.
| 0.85 | 0.4610 | 0.2611 |.
| 0.90 | 0.4743 | 0.2844 |.
| 0.95 | 0.4873 | 0.3085 |.
| 1.00 | 0.5000 | 0.3332 |.
| 1.05 | 0.5123 | 0.3585 |.
| 1.10 | 0.5244 | 0.3844 |.
| 1.15 | 0.5362 | 0.4109 |.
| 1.20 | 0.5477 | 0.4380 |.
| 1.25 | 0.5590 | 0.4657 |.
| 1.30 | 0.5701 | 0.4939 |.
| 1.35 | 0.5809 | 0.5227 |.
| 1.40 | 0.5916 | 0.5520 |.
| 1.45 | 0.6021 | 0.5818 |.
| 1.50 | 0.6124 | 0.6122 |.
| 1.55 | 0.6225 | 0.6431 |.
| 1.60 | 0.6325 | 0.6745 |.
| 1.65 | 0.6423 | 0.7063 |.
| 1.70 | 0.6519 | 0.7387 |.
| 1.75 | 0.6614 | 0.7715 |.
| 1.80 | 0.6708 | 0.8048 |.
| 1.85 | 0.6801 | 0.8386 |.
| 1.90 | 0.6892 | 0.8728 |.
| 1.95 | 0.6982 | 0.9075 |.
| 2.00 | 0.7071 | 0.9426 |.
| 2.05 | 0.7159 | 0.9782 |.
| 2.10 | 0.7246 | 1.0142 |.
| 2.15 | 0.7331 | 1.0507 |.
| 2.20 | 0.7416 | 1.0875 |.
| 2.25 | 0.7500 | 1.1248 |.
| 2.30 | 0.7583 | 1.1625 |.
| 2.35 | 0.7665 | 1.2007 |.
| 2.40 | 0.7746 | 1.2392 |.
| 2.45 | 0.7826 | 1.2781 |.
| 2.50 | 0.7906 | 1.3175 |.
| 2.55 | 0.7984 | 1.3572 |.
| 2.60 | 0.8062 | 1.3973 |.
| 2.65 | 0.8139 | 1.4378 |.
| 2.70 | 0.8216 | 1.4787 |.
| 2.75 | 0.8292 | 1.5200 |.
| 2.80 | 0.8367 | 1.5616 |.
| 2.85 | 0.8441 | 1.6036 |.
| 2.90 | 0.8515 | 1.6460 |.
| 2.95 | 0.8588 | 1.6888 |.
| 3.00 | 0.8660 | 1.7319 |.
| 3.05 | 0.8732 | 1.7754 |.
| 3.10 | 0.8803 | 1.8192 |.
| 3.15 | 0.8874 | 1.8634 |.
| 3.20 | 0.8944 | 1.9080 |.
| 3.25 | 0.9014 | 1.9528 |.
| 3.30 | 0.9083 | 1.9981 |.
| 3.35 | 0.9152 | 2.0437 |.
| 3.40 | 0.9220 | 2.0896 |.
| 3.45 | 0.9287 | 2.1359 |.
| 3.50 | 0.9354 | 2.1825 |.
| 3.55 | 0.9421 | 2.2294 |.
| 3.60 | 0.9487 | 2.2767 |.
| 3.65 | 0.9552 | 2.3243 |.
| 3.70 | 0.9618 | 2.3722 |.
| 3.75 | 0.9682 | 2.4205 |.
| 3.80 | 0.9747 | 2.4690 |.
| 3.85 | 0.9811 | 2.5179 |.
| 3.90 | 0.9874 | 2.5671 |.
| 3.95 | 0.9937 | 2.6167 |.
| 4.00 | 1.0000 | 2.6665 |.
| 4.05 | 1.0062 | 2.7167 |.
| 4.10 | 1.0124 | 2.7671 |.
| 4.15 | 1.0186 | 2.8179 |.
| 4.20 | 1.0247 | 2.8690 |.
| 4.25 | 1.0308 | 2.9204 |.
| 4.30 | 1.0368 | 2.9721 |.
| 4.35 | 1.0428 | 3.0241 |.
| 4.40 | 1.0488 | 3.0763 |.
| 4.45 | 1.0548 | 3.1289 |.
| 4.50 | 1.0607 | 3.1818 |.
| 4.55 | 1.0665 | 3.2350 |.
| 4.60 | 1.0724 | 3.2885 |.
| 4.65 | 1.0782 | 3.3422 |.
| 4.70 | 1.0840 | 3.3963 |.
| 4.75 | 1.0897 | 3.4506 |.
| 4.80 | 1.0954 | 3.5053 |.
| 4.85 | 1.1011 | 3.5602 |.
| 4.90 | 1.1068 | 3.6154 |.
| 4.95 | 1.1124 | 3.6709 |.
б) с использованием солвера ode45;
Файл-функция:.
function f=fqn (t, y).
b=2;
a=5;
x=(a/b)*sqrt (t);
f=x;
Файл-программа:.
[T, Y]=ode45('fqn',[0:0.05:5],[0]);
[T, Y].
plot (T, Y,'b*').
grid on.
xlabel ('t');
ylabel ('y');
Результат работы программы:.
ans =.
0 0.
0.0500 0.0183.
0.1000 0.0524.
0.1500 0.0965.
0.2000 0.1488.
0.2500 0.2080.
0.3000 0.2735.
0.3500 0.3448.
0.4000 0.4213.
0.4500 0.5028.
0.5000 0.5889.
0.5500 0.6795.
0.6000 0.7743.
0.6500 0.8731.
0.7000 0.9758.
0.7500 1.0822.
0.8000 1.1922.
0.8500 1.3058.
0.9000 1.4227.
0.9500 1.5429.
1.0000 1.6664.
1.0500 1.7929.
1.1000 1.9225.
1.1500 2.0551.
1.2000 2.1906.
1.2500 2.3289.
1.3000 2.4701.
1.3500 2.6139.
1.4000 2.7605.
1.4500 2.9097.
1.5000 3.0615.
1.5500 3.2159.
1.6000 3.3728.
1.6500 3.5321.
1.7000 3.6939.
1.7500 3.8581.
1.8000 4.0246.
1.8500 4.1935.
1.9000 4.3646.
1.9500 4.5381.
2.0000 4.7137.
2.0500 4.8916.
2.1000 5.0717.
2.1500 5.2539.
2.2000 5.4382.
2.2500 5.6247.
2.3000 5.8132.
2.3500 6.0038.
2.4000 6.1965.
2.4500 6.3911.
2.5000 6.5878.
2.5500 6.7864.
2.6000 6.9870.
2.6500 7.1895.
2.7000 7.3939.
2.7500 7.6003.
2.8000 7.8085.
2.8500 8.0186.
2.9000 8.2305.
2.9500 8.4443.
3.0000 8.6599.
3.0500 8.8773.
3.1000 9.0965.
3.1500 9.3175.
3.2000 9.5402.
3.2500 9.7647.
3.3000 9.9909.
3.3500 10.2189.
3.4000 10.4485.
3.4500 10.6798.
3.5000 10.9128.
3.5500 11.1475.
3.6000 11.3839.
3.6500 11.6219.
3.7000 11.8615.
3.7500 12.1027.
3.8000 12.3456.
3.8500 12.5901.
3.9000 12.8361.
3.9500 13.0838.
4.0000 13.3330.
4.0500 13.5838.
4.1000 13.8361.
4.1500 14.0900.
4.2000 14.3454.
4.2500 14.6023.
4.3000 14.8608.
4.3500 15.1208.
4.4000 15.3822.
4.4500 15.6452.
4.5000 15.9096.
4.5500 16.1755.
4.6000 16.4428.
4.6500 16.7117.
4.7000 16.9819.
4.7500 17.2537.
4.8000 17.5268.
4.8500 17.8014.
4.9000 18.0774.
4.9500 18.3548.
5.0000 18.6336.
в) с использованием системной функции feval.
Файл-функция:.
function f=fyn (x).
b=10;
a=5;
t=0:0.05:5;
x=(a/b).*sqrt (t);
f=x;
Файл-программа:.
figure.
fprintf ('Таблица значений (feval)n');
fprintf ('…n');
fprintf ('| t | x | y |n');
fprintf ('…n');
a=5;
b=10;
t=0:0.05:5;
x=(a/b).*sqrt (t);
y=feval ('fyn');
v=[t;x;y];
fprintf ('| %4.2f | %4.2f | %4.2f |n', v);
plot (t, x,'b*').
grid on.
hold on.
plot (t, y,'r+').
xlabel ('x');
ylabel ('y');
Результат работы программы:.
Таблица значений (feval).
….
| t | x | y |.
….
| 0.00 | 0.00 | 0.00 |.
| 0.05 | 0.11 | 0.11 |.
| 0.10 | 0.16 | 0.16 |.
| 0.15 | 0.19 | 0.19 |.
| 0.20 | 0.22 | 0.22 |.
| 0.25 | 0.25 | 0.25 |.
| 0.30 | 0.27 | 0.27 |.
| 0.35 | 0.30 | 0.30 |.
| 0.40 | 0.32 | 0.32 |.
| 0.45 | 0.34 | 0.34 |.
| 0.50 | 0.35 | 0.35 |.
| 0.55 | 0.37 | 0.37 |.
| 0.60 | 0.39 | 0.39 |.
| 0.65 | 0.40 | 0.40 |.
| 0.70 | 0.42 | 0.42 |.
| 0.75 | 0.43 | 0.43 |.
| 0.80 | 0.45 | 0.45 |.
| 0.85 | 0.46 | 0.46 |.
| 0.90 | 0.47 | 0.47 |.