{"id":5101,"date":"2025-04-19T14:27:08","date_gmt":"2025-04-19T10:57:08","guid":{"rendered":"https:\/\/projestaan.com\/mag\/?p=5101"},"modified":"2025-04-19T14:27:08","modified_gmt":"2025-04-19T10:57:08","slug":"pde-command-in-matlab","status":"publish","type":"post","link":"https:\/\/projestaan.com\/mag\/pde-command-in-matlab\/","title":{"rendered":"\u0622\u0645\u0648\u0632\u0634 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062f\u0633\u062a\u0648\u0631 pde \u062f\u0631 \u0645\u062a\u0644\u0628"},"content":{"rendered":"\t\t
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\u062f\u0633\u062a\u0648\u0631pde \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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\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u06cc\u0627 \u0645\u0639\u0627\u062f\u0644\u0627\u062aPDE \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0645 \u0631\u06cc\u0627\u0636\u06cc\u0627\u062a \u0648 \u0645\u0647\u0646\u062f\u0633\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u062f\u0644\u200c\u0633\u0627\u0632\u06cc \u067e\u062f\u06cc\u062f\u0647\u200c\u0647\u0627\u06cc \u0641\u06cc\u0632\u06cc\u06a9\u06cc \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0647\u0645\u0627\u0646\u0646\u062f \u0627\u0646\u062c\u0627\u0645 \u067e\u0631\u0648\u0698\u0647 \u0645\u06a9\u0627\u0646\u06cc\u06a9<\/a>\u060c \u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9 \u0633\u06cc\u0627\u0644\u0627\u062a \u0648 \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f. \u0646\u0631\u0645\u200c\u0627\u0641\u0632\u0627\u0631 \u0645\u062a\u0644\u0628 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062aPDE \u0627\u0628\u0632\u0627\u0631\u06cc \u0642\u0648\u06cc \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc\u200c\u0622\u0648\u0631\u062f \u0648 \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0642\u0627\u0628\u0644\u06cc\u062a\u200c\u0647\u0627\u06ccPDE \u062f\u0631 \u0645\u062a\u0644\u0628 \u0628\u0627\u06cc\u062fToolbox \u0645\u0631\u0628\u0648\u0637\u0647 \u0646\u0635\u0628 \u0634\u062f\u0647 \u0628\u0627\u0634\u062f. \u0628\u0627 \u0646\u0635\u0628 \u0628\u0648\u062f\u0646 \u0627\u06cc\u0646 Toolbox\u060c \u062f\u0633\u062a\u0648\u0631pde \u0627\u0645\u06a9\u0627\u0646 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0628\u0627 \u0628\u0627 \u0647\u0645\u0631\u0627\u0647 \u0628\u0627\u0634\u06cc\u062f \u062a\u0627 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u067e\u0631\u0648\u0698\u0647 \u0645\u062a\u0644\u0628<\/a> \u062e\u0648\u062f \u0628\u0627 \u062f\u0633\u062a\u0648\u0631 pde \u0622\u0634\u0646\u0627 \u0634\u0648\u06cc\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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\u0628\u062e\u0634 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u06a9\u062f \u0628\u0647 \u0634\u0631\u062d \u062c\u062f\u0648\u0644 \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

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\u0631\u062f\u06cc\u0641<\/p><\/td>

\u062a\u0648\u0636\u06cc\u062d<\/p><\/td>

\u062f\u0633\u062a\u0648\u0631<\/p><\/td><\/tr>

1<\/p><\/td>

\u0633\u0627\u062e\u062a \u0645\u062f\u0644:createpde \u00a0\u06cc\u06a9 \u0645\u062f\u0644 PDE \u00a0\u062c\u062f\u06cc\u062f \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0645\u062a\u063a\u06cc\u0631model \u00a0\u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p><\/td>

model = createpde<\/p><\/td><\/tr>

2<\/p><\/td>

\u062a\u0639\u0631\u06cc\u0641 \u0647\u0646\u062f\u0633\u0647 \u0645\u0633\u0627\u0644\u0647: \u0627\u0632 \u062a\u0627\u0628\u0639 geometryFromEdges \u00a0\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.geometry \u00a0\u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u062d\u0627\u0648\u06cc \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc \u0645\u0633\u062a\u0637\u06cc\u0644 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 geometryFromEdges \u00a0\u0647\u0646\u062f\u0633\u0647 \u0631\u0627 \u0628\u0647 \u0645\u062f\u0644 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p><\/td>

geometryFromEdges<\/p>

(model, geometry)<\/p><\/td><\/tr>

3<\/p><\/td>

\u062a\u0639\u06cc\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 PDE<\/p><\/td>

specifyCoefficients<\/p>

(model, \u2026 )<\/p><\/td><\/tr>

4<\/p><\/td>

\u062a\u0639\u06cc\u06cc\u0646 \u0634\u0631\u0627\u06cc\u0637 \u0645\u0631\u0632\u06cc<\/p><\/td>

applyBoundaryCondition<\/p>

(model, \u2026)<\/p><\/td><\/tr>

5<\/p><\/td>

\u0634\u0628\u06a9\u0647 \u0628\u0646\u062f\u06cc \u0645\u062f\u0644<\/p><\/td>

generateMesh(model)<\/p><\/td><\/tr>

6<\/p><\/td>

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647<\/p><\/td>

solvepde(model)<\/p><\/td><\/tr>

7<\/p><\/td>

\u0646\u0645\u0627\u06cc\u0634 \u0646\u062a\u0627\u06cc\u062c \u0628\u0647 \u0635\u0648\u0631\u062a \u06af\u0631\u0627\u0641\u06cc\u06a9\u06cc<\/p><\/td>

pdeplot(model,)<\/p><\/td><\/tr><\/tbody><\/table>\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\u0644 1: \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062f\u0633\u062a\u0648\u0631 pde \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u0648 \u0628\u0639\u062f\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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clc; clear;
model = createpde;

R1 = [3,4,-1,1,1,-1,0.5,0.5,-0.75,-0.75]’;
C1 = [1,0.5,-0.25,0.25]’;
C1 = [C1;zeros(length(R1) – length(C1),1)];
gm = [R1,C1];
sf = ‘R1-C1’;

ns = char(‘R1′,’C1’);
ns = ns’;
g = decsg(gm,sf,ns);

geometryFromEdges(model,g);
figure(1)
pdegplot(model,’EdgeLabels’,’on’)
axis equal
xlim([-1.1,1.1])

applyBoundaryCondition(model,’dirichlet’,’edge’,3,’u’,32);
applyBoundaryCondition(model,’dirichlet’,’edge’,1,’u’,72);
applyBoundaryCondition(model,’neumann’,’edge’,[2,4:8],’g’,-1);

specifyCoefficients(model,’m’,0,’d’,0,’c’,1,’a’,0,’f’,10);
generateMesh(model,’Hmax’,0.1);
results = solvepde(model);
u = results.NodalSolution;
figure(2)
pdeplot(model,’XYData’,u,’ZData’,u)
view(-23,8)<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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\u062e\u0631\u0648\u062c\u06cc \u06a9\u062f:<\/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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\u062a\u0648\u0636\u06cc\u062d \u06a9\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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\u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644\u060c \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0648\u0628\u0639\u062f\u06cc Pde \u0647\u0645\u0627\u0646\u0646\u062f \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u062f\u0631 \u0635\u0641\u062d\u0647 \u062f\u0648 \u0628\u0639\u062f\u06cc \u0628\u0631\u0631\u0633\u06cc \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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cmdel = createpde;<\/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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\u0627\u06cc\u0646 \u062e\u0637 \u06cc\u06a9 \u0645\u062f\u0644 \u062c\u062f\u06cc\u062f PDE \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0645\u062a\u063a\u06cc\u0631 cmdel \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\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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R1 = [3,4,-1,1,1,-1,0.5,0.5,-0.75,-0.75]’;
C1 = [1,0.5,-0.25,0.25]’;
C1 = [C1;zers(length(R1) – length(C1),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

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R1 : \u0645\u062e\u062a\u0635\u0627\u062a \u0648 \u0645\u0634\u062e\u0635\u0627\u062a \u06cc\u06a9 \u0645\u0633\u062a\u0637\u06cc\u0644 (\u0634\u06a9\u0644 \u0647\u0646\u062f\u0633\u06cc) \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\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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\u00a0C1: \u0645\u062e\u062a\u0635\u0627\u062a \u0648 \u0645\u0634\u062e\u0635\u0627\u062a \u06cc\u06a9 \u062f\u0627\u06cc\u0631\u0647 (\u06cc\u0627 \u0634\u06a9\u0644 \u062f\u06cc\u06af\u0631) \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\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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C1 = [C1;zers(length(R1) – length(C1),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

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gm = [R1,C1];
sf = ‘R1-C1’;<\/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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gm: \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0646\u062f\u0633\u06cc (gemetric matrix) \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0634\u0627\u0645\u0644 R1 \u0648 C1 \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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sf: \u06cc\u06a9 \u0631\u0634\u062a\u0647 \u0647\u0646\u062f\u0633\u06cc (gemetry string) \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 R1 \u0627\u0632 C1 \u06a9\u0633\u0631 \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

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ns = char(‘R1′,’C1’);
ns = ns’;

<\/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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ns: \u0646\u0627\u0645\u200c\u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u06a9\u0627\u0631\u0627\u06a9\u062a\u0631 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u062f.
‘;ns = ns
: \u0645\u0627\u062a\u0631\u06cc\u0633 \u0646\u0627\u0645\u200c\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0639\u0645\u0648\u062f\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc\u200c\u06a9\u0646\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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;g = decsg(gm,sf,ns)<\/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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\u0627\u06cc\u0646 \u062e\u0637 \u0647\u0646\u062f\u0633\u0647 \u0646\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0627\u0628\u0639 decsg \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0647\u0646\u062f\u0633\u0647 \u0627\u0635\u0644\u06cc \u0648 \u0631\u0648\u0627\u0628\u0637 \u0628\u06cc\u0646 \u0627\u0634\u06a9\u0627\u0644 \u0631\u0627 \u0645\u0634\u062e\u0635 \u0645\u06cc\u200c\u06a9\u0646\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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gemetryFrmEdges(mdel,g);<\/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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\u0647\u0646\u062f\u0633\u0647 \u0627\u06cc\u062c\u0627\u062f \u0634\u062f\u0647 \u0631\u0627 \u0628\u0647 \u0645\u062f\u0644 PDE \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u06a9\u0646\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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fpdegplt(mdel,’EdgeLabels’,’n’)<\/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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\u062f\u0633\u062a\u0648\u0631 \u0641\u0648\u0642\u060c \u0647\u0646\u062f\u0633\u0647 \u0645\u062f\u0644 \u0631\u0627 \u0631\u0633\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627\u06cc \u0644\u0628\u0647\u200c\u0647\u0627 \u0631\u0627 \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc\u200c\u062f\u0647\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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applyBundaryCnditin(mdel,’dirichlet’,’edge’,3,’u’,32);
applyBundaryCnditin(mdel,’dirichlet’,’edge’,1,’u’,72);
applyBundaryCnditin(mdel,’neumann’,’edge’,[2,4:8],’g’,-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

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\u0627\u06cc\u0646 \u062e\u0637\u0648\u0637 \u0634\u0631\u0627\u06cc\u0637 \u0645\u0631\u0632\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0645\u062f\u0644 PDE \u0627\u0639\u0645\u0627\u0644 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0627\u0648\u0644\u06cc\u0646 \u062e\u0637\u060c \u0634\u0631\u0627\u06cc\u0637 \u0645\u0631\u0632\u06cc \u062f\u06cc\u0631\u06cc\u06a9\u0644\u0647 (Dirichlet) \u0628\u0631\u0627\u06cc \u0644\u0628\u0647 3 \u0628\u0627 \u0645\u0642\u062f\u0627\u0631 32 \u0627\u0633\u062a. \u062f\u0648\u0645\u06cc\u0646 \u062e\u0637\u060c \u0634\u0631\u0627\u06cc\u0637 \u0645\u0631\u0632\u06cc \u062f\u06cc\u0631\u06cc\u06a9\u0644\u0647 \u0628\u0631\u0627\u06cc \u0644\u0628\u0647 1 \u0628\u0627 \u0645\u0642\u062f\u0627\u0631 72 \u0627\u0633\u062a. \u0633\u0648\u0645\u06cc\u0646 \u062e\u0637\u060c \u0634\u0631\u0627\u06cc\u0637 \u0645\u0631\u0632\u06cc \u0646\u06cc\u0648\u0645\u0646(Neumann) \u0628\u0631\u0627\u06cc \u0644\u0628\u0647\u200c\u0647\u0627\u06cc 2 \u0648 4 \u062a\u0627 8 \u0628\u0627 \u0645\u0642\u062f\u0627\u0631 -1 \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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specifyCefficients(mdel,’m’,0,’d’,0,’c’,1,’a’,0,’f’,10);<\/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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\u0627\u06cc\u0646 \u062e\u0637 \u0636\u0631\u0627\u06cc\u0628 \u0645\u0639\u0627\u062f\u0644\u0647 PDE \u0631\u0627 \u0645\u0634\u062e\u0635 \u0645\u06cc\u200c\u06a9\u0646\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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‘m’: \u0636\u0631\u06cc\u0628 \u0632\u0645\u0627\u0646\u060c ‘d’ : \u0636\u0631\u06cc\u0628 \u0641\u0636\u0627\u06cc\u06cc\u060c ‘c’ : \u0636\u0631\u06cc\u0628 \u0647\u0645\u06af\u0646\u060c ‘a’: \u0636\u0631\u06cc\u0628 \u063a\u06cc\u0631\u0647\u0645\u06af\u0646 \u0648 ‘f’ : \u062a\u0627\u0628\u0639 \u0645\u0646\u0628\u0639 \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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generateMesh(mdel,’Hmax’,0.1);<\/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

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\u0645\u0634 (\u0634\u0628\u06a9\u0647) \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u062d\u0644 PDE \u0631\u0627 \u0628\u0627 \u062d\u062f\u0627\u06a9\u062b\u0631 \u0627\u0646\u062f\u0627\u0632\u0647 \u0627\u0644\u0645\u0627\u0646 0.1 \u062a\u0648\u0644\u06cc\u062f \u0645\u06cc\u200c\u06a9\u0646\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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results = slvepde(mdel);<\/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\u0639\u0627\u062f\u0644\u0647 PDE \u0631\u0627 \u062d\u0644 \u06a9\u0631\u062f\u0647 \u0648 \u0646\u062a\u0627\u06cc\u062c \u0631\u0627 \u062f\u0631 \u0645\u062a\u063a\u06cc\u0631 results \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\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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u = results.NdalSlutin;<\/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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\u0631\u0627\u0647 \u062d\u0644 \u0646\u0648\u062f\u0627\u0644 (Ndal slutin) \u0645\u0639\u0627\u062f\u0644\u0647 PDE \u0631\u0627 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u06a9\u0631\u062f\u0647 \u0648 \u062f\u0631 \u0645\u062a\u063a\u06cc\u0631 u \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\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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pdeplt(mdel,’XYData’,u,’ZData’,u)<\/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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\u062f\u0633\u062a\u0648\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0646\u062a\u0627\u06cc\u062c \u0631\u0627 \u0628\u0631 \u0631\u0648\u06cc \u0634\u0628\u06a9\u0647 \u0647\u0646\u062f\u0633\u06cc \u0631\u0633\u0645 \u0645\u06cc\u200c\u06a9\u0646\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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\u0628\u0631\u0627\u06cc \u0622\u0634\u0646\u0627\u06cc\u06cc \u0628\u0627 \u0633\u0627\u06cc\u0631 \u062f\u0633\u062a\u0648\u0631\u0627\u062a \u0645\u0642\u0627\u0644\u0627\u062a \u0632\u06cc\u0631 \u0631\u0627 \u0628\u062e\u0648\u0627\u0646\u06cc\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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\u062f\u0633\u062a\u0648\u0631 find \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 double \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 abs \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 mod \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 for \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 diag \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 rem \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 reshape \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 round \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 mean \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr>

\u062f\u0633\u062a\u0648\u0631 floor \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/p><\/td><\/tr><\/tbody><\/table>\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":"

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