{"id":820557,"date":"2024-12-20T09:04:34","date_gmt":"2024-12-20T01:04:34","guid":{"rendered":"https:\/\/www.youtupa.com\/gonglue\/820557.html"},"modified":"2024-12-21T01:28:42","modified_gmt":"2024-12-20T17:28:42","slug":"matlab%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e8%a7%a3%e6%9e%90%e8%a7%a3_%e5%a6%82%e4%bd%95%e8%bd%bb%e6%9d%be%e6%b1%82%e8%a7%a3%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/www.youtupa.com\/gonglue\/820557.html","title":{"rendered":"MATLAB\u5fae\u5206\u65b9\u7a0b\u89e3\u6790\u89e3_\u5982\u4f55\u8f7b\u677e\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b"},"content":{"rendered":"
\"MATLAB\u5fae\u5206\u65b9\u7a0b\u89e3\u6790\u89e3_\u5982\u4f55\u8f7b\u677e\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\"<\/figure>\n

\u968f\u7740\u79d1\u6280\u7684\u4e0d\u65ad\u8fdb\u6b65\uff0c\u5fae\u5206\u65b9\u7a0b\u5728\u5404\u4e2a\u9886\u57df\u7684\u5e94\u7528\u8d8a\u6765\u8d8a\u5e7f\u6cdb\u3002\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\u662f\u4e00\u7c7b\u7279\u6b8a\u7684\u89e3\uff0c\u53ef\u4ee5\u63d0\u4f9b\u66f4\u52a0\u7cbe\u786e\u7684\u89e3\u6790\u7ed3\u679c\uff0c\u5bf9\u4e8e\u5206\u6790\u95ee\u9898\u5177\u6709\u91cd\u8981\u610f\u4e49\u3002\u5728\u89e3\u6790\u89e3\u5fae\u5206\u65b9\u7a0b\u65b9\u9762\uff0cMATLAB\u662f\u4e00\u4e2a\u975e\u5e38\u5f3a\u5927\u7684\u5de5\u5177\u3002<\/p>\n

\n

\u5fae\u5206\u65b9\u7a0b\u57fa\u7840<\/strong><\/p>\n

\u5fae\u5206\u65b9\u7a0b\u662f\u63cf\u8ff0\u81ea\u7136\u73b0\u8c61\u7684\u91cd\u8981\u6570\u5b66\u5de5\u5177\uff0c\u5b83\u53ef\u4ee5\u7528\u6765\u63cf\u8ff0\u7269\u7406\u3001\u5316\u5b66\u3001\u751f\u7269\u7b49\u5b66\u79d1\u4e2d\u7684\u73b0\u8c61\u3002\u5fae\u5206\u65b9\u7a0b\u53ef\u5206\u4e3a\u5e38\u5fae\u5206\u65b9\u7a0b\u548c\u504f\u5fae\u5206\u65b9\u7a0b\u4e24\u7c7b\u3002\u5e38\u5fae\u5206\u65b9\u7a0b\u662f\u53ea\u542b\u6709\u4e00\u4e2a\u81ea\u53d8\u91cf\u7684\u5fae\u5206\u65b9\u7a0b\uff0c\u800c\u504f\u5fae\u5206\u65b9\u7a0b\u5219\u542b\u6709\u591a\u4e2a\u81ea\u53d8\u91cf\u3002<\/p>\n

\u89e3\u6790\u89e3\u662f\u6307\u80fd\u591f\u7528\u5df2\u77e5\u7684\u57fa\u672c\u51fd\u6570\u8868\u793a\u51fa\u6765\u7684\u89e3\uff0c\u5b83\u662f\u5fae\u5206\u65b9\u7a0b\u7684\u4e00\u79cd\u7279\u6b8a\u89e3\u3002\u6c42\u89e3\u89e3\u6790\u89e3\u7684\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u5982\u53d8\u91cf\u5206\u79bb\u6cd5\u3001\u9f50\u6b21\u5316\u6cd5\u3001\u5e38\u6570\u53d8\u6613\u6cd5\u7b49\u3002<\/p>\n

MATLAB\u89e3\u6790\u89e3\u5de5\u5177\u7bb1<\/strong><\/p>\n

MATLAB\u63d0\u4f9b\u4e86\u5f88\u591a\u7528\u4e8e\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\u7684\u5de5\u5177\u7bb1\uff0c\u5982ODE\u5de5\u5177\u7bb1\u3001PDE\u5de5\u5177\u7bb1\u7b49\u3002ODE\u5de5\u5177\u7bb1\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u5e38\u5fae\u5206\u65b9\u7a0b\uff0c\u800cPDE\u5de5\u5177\u7bb1\u5219\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u504f\u5fae\u5206\u65b9\u7a0b\u3002<\/p>\n

\u4f7f\u7528MATLAB\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\u975e\u5e38\u7b80\u5355\uff0c\u53ea\u9700\u8981\u8c03\u7528\u76f8\u5e94\u7684\u51fd\u6570\u5373\u53ef\u3002\u4f8b\u5982\uff0c\u4f7f\u7528ODE\u5de5\u5177\u7bb1\u6c42\u89e3\u4e00\u9636\u7ebf\u6027\u5fae\u5206\u65b9\u7a0bdy\/dx+y=x\u7684\u89e3\u6790\u89e3\uff0c\u53ef\u4ee5\u4f7f\u7528MATLAB\u4e2d\u7684dsolve\u51fd\u6570\uff1a<\/p>\n

syms x y<\/code><\/p>\n

eqn = diff(y) + y == x;<\/code><\/p>\n

sol = dsolve(eqn, y(0) == 1);<\/code><\/p>\n

disp(sol);<\/code><\/p>\n

\u4f7f\u7528PDE\u5de5\u5177\u7bb1\u6c42\u89e3\u4e8c\u7ef4\u6cca\u677e\u65b9\u7a0b?2u=0\u7684\u89e3\u6790\u89e3\uff0c\u53ef\u4ee5\u4f7f\u7528MATLAB\u4e2d\u7684pdepe\u51fd\u6570\uff1a<\/p>\n

m = 0;<\/code><\/p>\n

x = linspace(0,1,101);<\/code><\/p>\n

t = linspace(0,1,101);<\/code><\/p>\n

u0 = sin(pi*x);<\/code><\/p>\n

[x,t,u] = pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t,u0);<\/code><\/p>\n

surf(x,t,u)<\/code><\/p>\n

\u5b9e\u4f8b\u5206\u6790<\/strong><\/p>\n

\u4e0b\u9762\u901a\u8fc7\u4e00\u4e2a\u5b9e\u4f8b\u6765\u6f14\u793a\u5982\u4f55\u4f7f\u7528MATLAB\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\u3002\u5047\u8bbe\u6709\u4e00\u4e2a\u4e00\u9636\u975e\u9f50\u6b21\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\uff1a<\/p>\n

dy\/dx + 2y = x+1<\/code><\/p>\n

\u5176\u4e2d\uff0cy(0)=1\u3002\u4f7f\u7528MATLAB\u4e2d\u7684dsolve\u51fd\u6570\u6c42\u89e3\u8be5\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\uff1a<\/p>\n

syms x y<\/code><\/p>\n

eqn = diff(y) + 2*y == x+1;<\/code><\/p>\n

sol = dsolve(eqn, y(0) == 1);<\/code><\/p>\n

disp(sol);<\/code><\/p>\n

\u8fd0\u884c\u7ed3\u679c\u4e3a\uff1a<\/p>\n

y(x) = (x^2 + 2*x + 3)\/4*exp(-2*x) + 1\/4<\/code><\/p>\n

\u53ef\u4ee5\u770b\u5230\uff0cMATLAB\u6c42\u89e3\u51fa\u4e86\u8be5\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\u3002\u4e0e\u4e4b\u5bf9\u6bd4\uff0c\u4f7f\u7528\u6570\u503c\u65b9\u6cd5\u6c42\u89e3\u540c\u6837\u7684\u5fae\u5206\u65b9\u7a0b\uff0c\u7ed3\u679c\u53ef\u80fd\u4f1a\u6709\u8bef\u5dee\u3002<\/p>\n

\u89e3\u6790\u89e3\u4e0e\u6570\u503c\u89e3\u7684\u5dee\u5f02\u4e3b\u8981\u5728\u4e8e\u7cbe\u5ea6\u548c\u8ba1\u7b97\u901f\u5ea6\u3002\u89e3\u6790\u89e3\u53ef\u4ee5\u63d0\u4f9b\u66f4\u52a0\u7cbe\u786e\u7684\u7ed3\u679c\uff0c\u4f46\u6c42\u89e3\u8fc7\u7a0b\u53ef\u80fd\u6bd4\u6570\u503c\u65b9\u6cd5\u590d\u6742\u3002\u800c\u6570\u503c\u65b9\u6cd5\u5219\u53ef\u4ee5\u5feb\u901f\u6c42\u89e3\uff0c\u4f46\u7ed3\u679c\u53ef\u80fd\u5b58\u5728\u8bef\u5dee\u3002<\/p>\n

\u7ed3\u8bba<\/strong><\/p>\n

MATLAB\u5728\u89e3\u6790\u89e3\u5fae\u5206\u65b9\u7a0b\u65b9\u9762\u5177\u6709\u5f88\u5927\u7684\u4f18\u52bf\u548c\u5e94\u7528\u4ef7\u503c\u3002MATLAB\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u5de5\u5177\u7bb1\uff0c\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u5e38\u5fae\u5206\u65b9\u7a0b\u548c\u504f\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\u3002\u89e3\u6790\u89e3\u53ef\u4ee5\u63d0\u4f9b\u66f4\u52a0\u7cbe\u786e\u7684\u7ed3\u679c\uff0c\u5bf9\u4e8e\u5206\u6790\u95ee\u9898\u5177\u6709\u91cd\u8981\u610f\u4e49\u3002\u4f46\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9700\u8981\u6839\u636e\u5177\u4f53\u95ee\u9898\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u3002<\/p>\n

\u672a\u6765\uff0c\u968f\u7740\u79d1\u6280\u7684\u4e0d\u65ad\u8fdb\u6b65\uff0cMATLAB\u5728\u5fae\u5206\u65b9\u7a0b\u6c42\u89e3\u4e2d\u7684\u5e94\u7528\u5c06\u4f1a\u8d8a\u6765\u8d8a\u5e7f\u6cdb\u3002\u6211\u4eec\u6709\u7406\u7531\u76f8\u4fe1\uff0cMATLAB\u5c06\u4f1a\u6210\u4e3a\u5fae\u5206\u65b9\u7a0b\u6c42\u89e3\u9886\u57df\u7684\u91cd\u8981\u5de5\u5177\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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