{"id":4836,"date":"2025-05-08T14:44:29","date_gmt":"2025-05-08T11:14:29","guid":{"rendered":"https:\/\/projestaan.com\/mag\/?p=4836"},"modified":"2025-05-08T15:31:49","modified_gmt":"2025-05-08T12:01:49","slug":"solving-the-equation-in-matlab","status":"publish","type":"post","link":"https:\/\/projestaan.com\/mag\/solving-the-equation-in-matlab\/","title":{"rendered":"\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0631 \u0645\u062a\u0644\u0628 | \u0645\u0639\u0631\u0641\u06cc 4 \u0631\u0648\u0634 \u0647\u0645\u0631\u0627\u0647 \u0645\u062b\u0627\u0644"},"content":{"rendered":"\t\t
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\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0631 \u0645\u062a\u0644\u0628<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\u0622\u06af\u0627\u0647\u06cc \u0627\u0632 \u0646\u062d\u0648\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0646\u0631\u0645 \u0627\u0641\u0632\u0627\u0631 \u0645\u062a\u0644\u0628 \u0644\u0627\u0632\u0645\u0647 \u0627\u0646\u062c\u0627\u0645 \u067e\u0631\u0648\u0698\u0647 \u062f\u0631 \u0645\u062a\u0644\u0628<\/a> \u0645\u06cc \u0628\u0627\u0634\u062f. \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 \u0645\u0642\u0627\u0644\u0627\u062a \u0645\u0648\u0633\u0633\u0647 \u067e\u0631\u0648\u0698\u0633\u062a\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f. \u0627\u06af\u0631 \u0645\u06cc\u062e\u0648\u0627\u0647\u06cc\u062f \u0645\u0637\u0627\u0644\u0628 \u06af\u0633\u062a\u0631\u062f\u0647 \u0627\u0632 \u0645\u062a\u0644\u0628 \u0631\u0627 \u0641\u0631\u0627\u0628\u06af\u06cc\u0631\u06cc\u062f\u060c \u0648\u0628\u0633\u0627\u06cc\u062a tutorialspoint<\/a> \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0645\u06cc \u0634\u0648\u062f.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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1- \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc<\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\u0645\u062b\u0627\u06441- \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0627\u062a\u0631\u06cc\u0633<\/h3>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a (Ax = b) \u0645\u062f\u0644 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646A \u0645\u0627\u062a\u0631\u06cc\u0633 \u0636\u0631\u0627\u06cc\u0628 \u0648 b \u0628\u0631\u062f\u0627\u0631 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062b\u0627\u0628\u062a \u0627\u0633\u062a.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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clc; clear; close all
A = [13 20; 1 25];
b = [51; 125];
x = A\\b;
disp(x);<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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\u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0646\u0627\u0645\u0647:<\/strong><\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\u00a0 -4.0164
\u00a0 5.1607<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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\u062a\u0648\u0636\u06cc\u062d: \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0639\u0645\u0644\u06af\u0631 \\ \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u062a\u0648\u0633\u0637 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.

\u0627\u06af\u0631 \u0645\u06cc\u062e\u0648\u0627\u0647\u06cc\u062f \u0627\u0632 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0631\u0627\u06cc \u062d\u0627\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u062e\u0648\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f \u0628\u0627\u06cc\u062f \u0628\u0627 \u0645\u0628\u062d\u062b \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0647 \u062d\u062f \u06a9\u0627\u0641\u06cc \u0622\u0634\u0646\u0627 \u0628\u0627\u0634\u06cc\u062f. \u0645\u0637\u0627\u0644\u0639\u0647 \u0645\u0642\u0627\u0644\u0627\u062a \u0632\u06cc\u0631 \u0628\u0631\u0627\u06cc \u0639\u0644\u0627\u0642\u0647 \u0645\u0646\u062f\u0627\u0646 \u0628\u0647 \u0645\u0628\u062d\u062b \u0645\u0627\u062a\u0631\u06cc\u0633 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0645\u06cc \u0634\u0648\u062f:

1- \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0645\u0627\u0646\u06cc \u062f\u0631 \u0645\u062a\u0644\u0628<\/a>
2- \u0622\u0645\u0648\u0632\u0634 \u0627\u06cc\u062c\u0627\u062f \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0631 \u0645\u062a\u0644\u0628<\/a>
3- \u062a\u063a\u06cc\u06cc\u0631 \u0634\u06a9\u0644 \u0648 \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u062a\u0644\u0628 \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633<\/a>
4- \u0646\u062d\u0648\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u0637\u0631\u06cc \u0628\u0647 \u0633\u062a\u0648\u0646\u06cc \u0648 \u0628\u0631\u0639\u06a9\u0633 \u062f\u0631 \u0645\u062a\u0644\u0628<\/a>
5- \u0686\u06af\u0648\u0646\u06af\u06cc \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0631 MATLAB<\/a>
6- \u062a\u0642\u0633\u06cc\u0645 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627 \u062f\u0631 Matlab<\/a>

<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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\u0645\u062b\u0627\u06442- \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 \u0633\u0627\u06cc\u0631 \u0631\u0648\u0634\u0647\u0627<\/h3>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0631\u0648\u0634\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u06cc\u0645 \u06cc\u0627 \u062a\u06a9\u0631\u0627\u0631\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. \u0631\u0648\u0634 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0645\u0633\u062a\u0642\u06cc\u0645 \u0645\u062b\u0644 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u0630\u0641 \u06af\u0627\u0648\u0633 \u0648 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631\u06cc \u0645\u062b\u0644 \u0631\u0648\u0634 \u0698\u0627\u06a9\u0648\u0628\u06cc \u0648 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u0627\u0633\u062a.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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clc; clear; close all
A = [13 20; 1 25];
b = [51; 125];
x0=[0;0];
tol=0.001;
maxIter=100;
x = jacobi(A, b, x0, tol, maxIter);
disp(x)<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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% \u062a\u0639\u0631\u06cc\u0641 \u062a\u0627\u0628\u0639 \u0698\u0627\u06a9\u0648\u067e\u06cc<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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function x = jacobi(A, b, x0, tol, maxIter)
n = length(b);
x = x0;
for k = 1:maxIter
x_new = zeros(n, 1);
for i = 1:n
sum1 = A(i, 1:i-1)*x(1:i-1);
sum2 = A(i, i+1:n)*x(i+1:n);
x_new(i) = (b(i) – sum1 – sum2) \/ A(i, i);
end
if norm(x_new – x, inf) < tol
break;
end
x = x_new;
end
end<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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\u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0646\u0627\u0645\u0647:<\/strong><\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\u00a0-4.0163
\u00a05.1606<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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\u062a\u0648\u0636\u06cc\u062d: \u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0627\u0632 \u0631\u0648\u0634 \u0698\u0627\u06a9\u0648\u0628\u06cc \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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2. \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u063a\u06cc\u0631\u062e\u0637\u06cc<\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\u0645\u0639\u0645\u0648\u0644\u0627 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0631\u0648\u0634 \u0646\u06cc\u0648\u062a\u0646-\u0631\u0627\u0641\u0633\u0648\u0646 \u0648 \u0631\u0648\u0634 \u0628\u06cc\u0632\u06cc\u0631 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u0645\u062b\u0627\u06443- \u0631\u0648\u0634 \u0646\u06cc\u0648\u062a\u0646-\u0631\u0627\u0641\u0633\u0648\u0646<\/h3>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u063a\u06cc\u0631\u062e\u0637\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a (f(x) = 0) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0631\u0648\u0634 \u0646\u06cc\u0648\u062a\u0646-\u0631\u0627\u0641\u0633\u0648\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

clc; clear; close all
f = @(x) x^3 – 12*x; % \u062a\u0627\u0628\u0639
df = @(x) 3*x^2-12; % \u0645\u0634\u062a\u0642 \u062a\u0627\u0628\u0639
x0 = 1; % \u062d\u062f\u0633 \u0627\u0648\u0644\u06cc\u0647
tol = 1e-3;
maxIter = 150;
x = x0;
for k = 1:maxIter
x_new = x – f(x) \/ df(x);
if abs(x_new – x) < tol
break;
end
x = x_new;
end
disp(x);<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0646\u0627\u0645\u0647:<\/strong><\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u00a0 -1.0584e-09<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062a\u0648\u0636\u06cc\u062d: \u062a\u0648\u062c\u0647 \u0634\u0648\u062f \u06a9\u0647 \u062c\u0648\u0627\u0628 \u0645\u062b\u0627\u0644 \u0646\u0632\u062f\u06cc\u06a9 \u0635\u0641\u0631 \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0635\u0648\u0631\u062a \u0645\u0633\u0627\u0644\u0647 \u0647\u0645 \u0645\u0634\u062e\u0635 \u0628\u0648\u062f \u06a9\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u062c\u0648\u0627\u0628\u0647\u0627\u06cc \u0645\u0633\u0627\u0644\u0647 \u0635\u0641\u0631 \u0627\u0633\u062a.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u0645\u062b\u0627\u06444- \u0631\u0648\u0634 \u0628\u06cc\u0632\u06cc\u0631(\u0631\u0648\u0634 \u0642\u062f\u0631\u062a\u0645\u0646\u062f \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u063a\u06cc\u0631\u062e\u0637\u06cc)<\/h3>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

clc; clear; close all
f = @(x) 5*x^3 – 2*x – 2; % \u062a\u0627\u0628\u0639
x0 = 1; % \u062d\u062f\u0633 \u0627\u0648\u0644\u06cc\u0647
tol = 1e-4;
maxIter = 150;
x = fzero(f, x0);
disp(x);<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0646\u0627\u0645\u0647:<\/strong><\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u00a0 0.9150<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062a\u0648\u0636\u06cc\u062d: \u0628\u0627 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0646 \u062c\u0648\u0627\u0628 \u0645\u062b\u0627\u0644 \u062f\u0631 \u062a\u0627\u0628\u0639 \u0627\u0648\u0644\u06cc\u0647 \u0635\u062d\u062a \u062e\u0631\u0648\u062c\u06cc \u0642\u0627\u0628\u0644 \u0627\u0633\u062a.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u00a03. \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644<\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0645\u0639\u0645\u0648\u0644\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u067e\u0631\u06a9\u0627\u0631\u0628\u0631\u062f ode45, ode23 \u0648 \u063a\u06cc\u0631\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u0645\u062b\u0627\u06445- \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0645\u0639\u0645\u0648\u0644\u06cc (ODE) \u0628\u0627 \u0631\u0648\u0634 ode45<\/h3>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

clc; clear; close all
% \u062a\u0639\u0631\u06cc\u0641 \u062a\u0627\u0628\u0639 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644
f = @(t, y) -12*y + t^2 + 1;
tspan = [0 2];
y0 = 0;
[t, y] = ode45(f, tspan, y0);
plot(t, y);
xlabel(‘t’);
ylabel(‘y’);
title(‘Solving diff Eq.’)
grid on<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0646\u0627\u0645\u0647:<\/strong><\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a\t\t\t\t\t\t\t\t\t\t\t
\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0645\u0639\u0645\u0648\u0644\u06cc (ODE) \u0628\u0627 \u0631\u0648\u0634 ode45<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062a\u0648\u0636\u06cc\u062d: \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u00a0 dy\/dt=-12*y + t^2 + 1;<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0634\u0631\u0627\u06cc\u0637 \u0627\u0648\u0644\u06cc\u0647 y0=0 \u0648 \u0645\u062f\u062a \u0632\u0645\u0627\u0646 \u0634\u0628\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0627\u0632 \u0632\u0645\u0627\u0646 tspan =[0,2] \u0627\u0633\u062a.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u0645\u062b\u0627\u06446- \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0645\u0639\u0645\u0648\u0644\u06cc (ODE) \u0628\u0627 \u0631\u0648\u0634 ode23<\/h3>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

clc; clear; close all
% \u062a\u0639\u0631\u06cc\u0641 \u062a\u0627\u0628\u0639 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644
f = @(t, y) -y^2 + t*sin(t);
tspan = [1 4];
y0 = 1;
[t, y] = ode23(f, tspan, y0);
plot(t, y);
xlabel(‘t’);
ylabel(‘y’);
title(‘Solving diff Eq.’)
grid on<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0646\u0627\u0645\u0647:<\/strong><\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a\t\t\t\t\t\t\t\t\t\t\t
\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0645\u0639\u0645\u0648\u0644\u06cc (ODE) \u0628\u0627 \u0631\u0648\u0634 ode23<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062a\u0648\u0636\u06cc\u062d: \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u00a0 dy\/dt= -y^2 + t*sin(t);<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0634\u0631\u0627\u06cc\u0637 \u0627\u0648\u0644\u06cc\u0647 y0=1 \u0648 \u0645\u062f\u062a \u0632\u0645\u0627\u0646 \u0634\u0628\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0627\u0632 \u0632\u0645\u0627\u0646 tspan =[ 1 4] \u0627\u0633\u062a.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

4- \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc (PDE)<\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u0645\u0627\u0646\u0646\u062f \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644\u0627\u062a \u0645\u062d\u062f\u0648\u062f \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

\u0645\u062b\u0627\u06447- \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633<\/h3>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t

clc; clear; close all
% \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u0647\u0627
L = 10; % \u0637\u0648\u0644 \u062f\u0627\u0645\u0646\u0647
Nx = 50; % \u062a\u0639\u062f\u0627\u062f \u0646\u0642\u0627\u0637 \u062f\u0631 \u062c\u0647\u062a x
dx = L \/ (Nx-1); % \u0641\u0627\u0635\u0644\u0647 \u0628\u06cc\u0646 \u0646\u0642\u0627\u0637
% \u0645\u0627\u062a\u0631\u06cc\u0633 \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0627\u0648\u0644\u06cc\u0647
u = 0.85*ones(Nx, 1);
u_new = zeros(Nx, 1);
alpha = 0.01;
for t = 1:1000
for i = 2:Nx-1
u_new(i) = u(i) + alpha * (u(i+1) – 2*u(i) + u(i-1));
end
u = u_new;
end
x = linspace(0, L, Nx);
plot(x, u);
xlabel(‘x’);
ylabel(‘u’);
title(‘Laplace Eq Solving’);
grid on<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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\u062e\u0631\u0648\u062c\u06cc \u0628\u0631\u0646\u0627\u0645\u0647:<\/strong><\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\n\t\t\t\t\t\t\t\t\t\t\"\u062d\u0644\t\t\t\t\t\t\t\t\t\t\t
\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\u062a\u0648\u0636\u06cc\u062d: \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0636\u0631\u0627\u06cc\u0628 \u0648 \u062a\u0639\u0631\u06cc\u0641 \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0627\u06cc\u0646 \u0645\u0633\u0627\u0644\u0647 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u062a\u0639\u0631\u06cc\u0641 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u0639\u062f\u062f\u06cc \u0642\u0627\u0628\u0644 \u062d\u0644 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0637\u0648\u0644 \u0641\u0636\u0627\u06cc \u0645\u0633\u0627\u0644\u0647 (L) \u0648 \u062a\u0639\u062f\u0627\u062f \u0646\u0642\u0627\u0637 (N) \u0627\u0633\u062a \u0648 \u0634\u0631\u0627\u06cc\u0637 \u0627\u0648\u0644\u06cc\u0647 0.85 \u0627\u0633\u062a.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0631 \u0645\u062a\u0644\u0628 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u0631 \u0645\u0628\u0627\u062d\u062b \u0645\u062e\u062a\u0644\u0641 \u0645\u0647\u0646\u062f\u0633\u06cc \u0646\u0642\u0634 \u0627\u0633\u0627\u0633\u06cc \u062f\u0627\u0631\u0646\u062f. \u062f\u0631 \u0639\u0644\u0648\u0645 \u0645\u0647\u0646\u062f\u0633\u06cc \u0648 \u0641\u06cc\u0632\u06cc\u06a9\u060c \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062f\u0631 \u0645\u062f\u0644\u200c\u0633\u0627\u0632\u06cc \u0633\u06cc\u0633\u062a\u0645\u200c\u0647\u0627\u06cc \u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9\u06cc \u0648 \u062f\u0631 \u0639\u0644\u0648\u0645 \u062f\u0627\u062f\u0647 \u0648 \u0622\u0645\u0627\u0631\u060c \u062a\u062d\u0644\u06cc\u0644 \u0648 \u067e\u06cc\u0634\u200c\u0628\u06cc\u0646\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u062f\u0644\u200c\u0647\u0627\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0648 \u0622\u0645\u0627\u0631\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u067e\u0630\u06cc\u0631\u062f. \u062d\u0644 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u06a9\u0646\u06cc\u06a9\u200c\u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0627\u0645\u06a9\u0627\u0646\u200c\u067e\u0630\u06cc\u0631 \u0627\u0633\u062a. […]<\/p>\n","protected":false},"author":5,"featured_media":4872,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rank_math_lock_modified_date":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4836","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matlab-training"],"views":717,"_links":{"self":[{"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/posts\/4836","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/comments?post=4836"}],"version-history":[{"count":40,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/posts\/4836\/revisions"}],"predecessor-version":[{"id":5534,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/posts\/4836\/revisions\/5534"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/media\/4872"}],"wp:attachment":[{"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/media?parent=4836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/categories?post=4836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/tags?post=4836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}