用PDE Toolbox求解三类典型方程求解抛物型方程Word文档下载推荐.docx
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区域设置单击工具
，在窗口拖拉出一个矩形，双击矩形区域，在对话框中输入Left为-0.5，Bottom为-0.8，Width为1，Height为1.6，单击OK按钮，显示矩形区域R1。
用同样方法做内孔R2，只要设置Left为-00.5，Bottom为-0.4，Width为0.1，Height为0.8即可。
然后在栏中键入R1-R2。
第二步：
设置边界条件单击工具
，图形边界变红，逐段双击边界，打开BoundaryCondition对话框，输入边界条件。
对于同一类型的边界，可按shift键，将多个边界同时选择，统一设置边界条件。
本题在左边界上选择Dirichlet条件，输入h为1，r为100；
右边界上，选择Neumann条件，输入g为-1，q为0；
其他边界上，选择Neumann条件，输入g为0，q为0。
第三步：
设置方程类型单击PDE菜单中PDESpecification…选项，打开PDESpecification对话框，选择方程类型。
本题单击Parabolic（抛物型），输入d为1,c为1，a为0，f为0，然后单击OK按钮。
第四步：
网格剖分单击工具
，或者单击Mesh菜单中InitializeMesh选项，可进行初始网格剖分，如果需要网格加密，再单击
，或者单击Mesh菜单中RefineMesh选项。
第五步：
初值和误差设置单击Solve菜单中Parameters…选项，打开SolveParameters…对话框，输入Time为0：
5，u（t0）为0，Relativetolerance为0.01，Absolutetolerance为0.001，然后单击OK按钮。
第六步：
解的图形单击Plot菜单中Parameters…选项，出现PlotSelection对话框，从中可以选择Color,Contour,Arrows,Deformedmesh,Height（3-Dplot），还可以设置等值线的数目等。
本例中选择Color,Contour和Arrows三项，然后单击Plot按钮，窗口显示出时的解的彩色图形。
第七步：
数值解的输出单击Solve菜单中ExportSolution选项，在打开的Export对话框中输入u，单击OK按钮确定。
再在MATLAB命令窗口键入u，按回车键确定，即显示按节点编号排列的数值解
>
u
u=
079.629195.377498.038098.570698.6395
079.629295.377498.038098.570598.6395
100.0000100.0000100.0000100.0000100.0000100.0000
083.357796.385898.586999.027599.0845
083.365396.387498.587599.027999.0849
089.818897.811199.161399.431599.4664
089.811897.809699.160799.431099.4660
079.332495.313998.013998.554498.6243
078.559295.146297.948698.509698.5822
077.504594.917197.859298.448298.5244
076.590594.720097.783398.396798.4760
076.247094.643297.751698.374098.4545
076.572894.716797.782598.396398.4757
077.499694.916097.858798.447898.5241
078.557595.145897.948598.509598.5821
079.331195.313698.013898.554398.6243
080.302095.620698.208698.726698.7936
082.123196.082598.440898.912898.9739
084.960796.739198.728899.127199.1786
088.503697.527199.051599.356599.3960
092.353498.364499.379899.583099.6093
096.194999.189099.694899.795999.8090
080.325695.716398.316798.837298.9046
078.183495.245098.127898.705098.7796
077.157895.020298.038498.642798.7209
077.155295.019698.038198.642598.7207
078.180195.244198.127398.704698.7792
080.324495.715998.316598.837198.9044
096.194699.188999.694799.795999.8090
092.353298.364399.379799.582999.6092
088.510197.528299.051699.356599.3959
084.949196.736998.728399.126999.1784
082.118996.081798.440598.912798.9738
080.301895.620698.208698.726698.7936
092.781198.458999.418099.609899.6347
094.801098.899199.591299.729699.7476
095.720199.098699.669299.783299.7980
095.724399.099599.669599.783599.7982
094.808998.900899.591999.730199.7480
092.784298.459699.418299.610099.6348
096.123199.179199.695299.798499.8118
077.913995.144398.055698.638598.7139
096.236699.203499.704599.804799.8176
077.828795.123898.046198.631198.7068
081.275295.891498.360798.855098.9190
093.190298.544999.449599.630499.6539
093.123698.530699.443999.626799.6503
081.315595.901198.365398.858598.9224
097.027799.375099.771499.850699.8609
076.689794.877297.950398.565798.6452
086.442797.071398.866899.226299.2727
086.820097.155098.900999.250399.2955
078.450695.222498.056298.623598.6969
096.920299.346199.755899.837899.8484
096.958299.354299.758999.839899.8503
078.430095.217198.053498.621298.6947
077.254295.027098.030098.631398.7090
095.976399.151799.687999.795199.8090
077.304295.038498.034998.634998.7125
095.922999.140299.683599.792199.8062
083.671896.446598.604799.036799.0926
090.245097.907199.201499.460499.4940
090.022897.858899.182599.447399.4816
083.502696.407698.587799.024199.0806
097.579399.490099.812799.877299.8855
076.857094.884997.931098.540998.6198
076.715894.845897.909298.522698.6019
097.844499.546299.833699.891099.8985
080.115795.579298.191798.714798.7823
096.272899.205699.701099.800299.8130
096.292399.209899.702699.801299.8140
080.121395.580998.192798.715598.7832
093.695198.656299.494199.661899.6835
079.902395.607098.260498.791698.8604
093.743098.666599.498299.664599.6861
079.861295.597698.256498.788798.8576
086.528697.088398.872299.229399.2755
086.666397.118898.884699.238099.2837
089.667997.780399.150799.424999.4604
083.904696.502998.631399.057399.1125
083.778796.474598.619499.048799.1042
089.521997.748399.138099.416199.4521
096.770299.312499.741899.827799.8388
079.458595.432098.130798.670998.7408
096.750099.308199.740299.826699.8378
079.452295.430198.129698.670098.7399
098.211999.622199.860399.907999.9141
077.268694.939197.924898.522598.5999
098.129899.604799.853899.903699.9100
077.312794.951297.931598.528298.6054
076.406294.750197.849798.470398.5506
098.591699.704099.891899.929499.9342
096.088299.176999.698599.802799.8162
076.963194.968998.011498.620598.6993
078.597395.326698.153298.719198.7923
094.670598.869199.578299.720199.7385
078.554095.316898.149198.716198.7895
094.716098.879099.582199.722799.7409
081.384695.904598.357598.848598.9120
093.567798.625899.480299.651199.6733
081.356495.897598.354198.845898.9094
093.622598.637699.484799.654299.6762
086.337397.046998.856199.218299.2651
087.034297.201898.919499.263299.3077
094.409298.807699.550599.699299.7184
080.116295.627698.248298.772998.8407
080.138695.632998.250898.774898.8426
094.374298.800199.547699.697299.7166
079.788195.463098.111298.641398.7099
098.115999.598799.849199.899299.9057
098.119899.599599.849499.899499.9059
079.788895.463298.111498.641498.7100
087.959197.406099.001999.321299.3626
085.464996.851698.775299.160299.2100
099.107199.812299.931399.955199.9582
076.427994.728897.821298.440398.5204
082.053996.085798.456498.930998.9923
091.561898.192299.312299.536399.5653
082.013396.076598.452498.928098.9896
091.611398.202999.316499.539299.5681
083.967296.518298.638699.063099.1179
089.345197.708099.120799.403499.4400
083.906096.504498.632999.058999.1140
089.413697.723099.126799.407699.4439
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