{"id":35,"date":"2025-12-20T02:00:58","date_gmt":"2025-12-19T18:00:58","guid":{"rendered":"http:\/\/www.ex-5.com\/?p=35"},"modified":"2025-12-20T02:00:58","modified_gmt":"2025-12-19T18:00:58","slug":"%e6%a4%8d%e7%89%a9%e6%b0%ae%e7%b4%a0%e5%90%b8%e6%94%b6%e5%8f%8a%e5%9c%9f%e5%a3%a4%e6%b0%ae%e7%b4%a0%e8%bd%ac%e5%8c%96%e8%bf%81%e7%a7%bb-matlab-%e6%a8%a1%e6%8b%9f%e6%96%b9%e6%a1%88","status":"publish","type":"post","link":"http:\/\/www.ex-5.com\/?p=35","title":{"rendered":"\u690d\u7269\u6c2e\u7d20\u5438\u6536\u53ca\u571f\u58e4\u6c2e\u7d20\u8f6c\u5316\u8fc1\u79fb MATLAB \u6a21\u62df\u65b9\u6848"},"content":{"rendered":"\n<p>\u690d\u7269\u6c2e\u7d20\u5438\u6536\u53ca\u571f\u58e4\u6c2e\u7d20\u8f6c\u5316\u8fc1\u79fb MATLAB \u6a21\u62df\u65b9\u6848\uff08\u6574\u5408\u7248\uff09<\/p>\n\n\n\n<p>\u4e00\u3001 \u6a21\u578b\u6838\u5fc3\u6846\u67b6<\/p>\n\n\n\n<p>\u6a21\u578b\u5206\u4e3a \u571f\u58e4\u6c2e\u7d20\u8f6c\u5316\u3001\u690d\u7269\u6839\u7cfb\u5438\u6536\u3001\u6c2e\u7d20\u8fc1\u79fb \u4e09\u4e2a\u6838\u5fc3\u6a21\u5757\uff0c\u7ed3\u5408\u76d0\u6e0d\u571f\u7279\u6027\u52a0\u5165\u76d0\u5206\u6291\u5236\u4fee\u6b63\u9879\uff0c\u91c7\u7528\u5fae\u5206\u65b9\u7a0b\u7ec4\u63cf\u8ff0\u8fc7\u7a0b\uff0c\u901a\u8fc7 MATLAB \u7684 pdepe \u51fd\u6570\uff08\u504f\u5fae\u5206\u65b9\u7a0b\u6c42\u89e3\uff09\u6216 ode45 \u51fd\u6570\uff08\u5e38\u5fae\u5206\u65b9\u7a0b\u6c42\u89e3\uff09\u5b9e\u73b0\u6a21\u62df\u3002<\/p>\n\n\n\n<p>1. &nbsp;\u571f\u58e4\u6c2e\u7d20\u8f6c\u5316\u6a21\u5757\uff08\u4e00\u7ea7\u52a8\u529b\u5b66\u65b9\u7a0b\uff09<\/p>\n\n\n\n<p>\u2022 \u6c28\u5316\u8fc7\u7a0b\uff1a\u6709\u673a\u6c2e\u8f6c\u5316\u4e3a\u94f5\u6001\u6c2e<\/p>\n\n\n\n<p>\\(\\frac{dOrgN}{dt} = -k_{amm} \\cdot OrgN \\)<\/p>\n\n\n\n<p>\u2022 \u785d\u5316\u8fc7\u7a0b\uff1a\u5206\u4e24\u6b65\uff0c\u94f5\u6001\u6c2e\u2192\u4e9a\u785d\u6001\u6c2e\u2192\u785d\u6001\u6c2e\uff08\u52a0\u5165\u76d0\u5206\u5bf9\u7b2c\u4e8c\u6b65\u7684\u4fee\u6b63\uff09<\/p>\n\n\n\n<p>\\(\\frac{dNH_4}{dt} = k_{amm} \\cdot OrgN &#8211; k_{n1} \\cdot NH_4\\)<\/p>\n\n\n\n<p>\\(k_{n2}(S) = (39.59 \\cdot (\\ln S)^2 &#8211; 244.27 \\cdot \\ln S + 393.86) \\times 10^{-3} \\)<\/p>\n\n\n\n<p>$latex\\frac{dNO_3}{dt} = k_{n1} \\cdot NH_4 &#8211; k_{n2}(S) \\cdot NO_3$<\/p>\n\n\n\n<p>\u2022 \u53c2\u6570\u8bf4\u660e<\/p>\n\n\n\n<p>\u25e6 \\(k_{amm}\uff1a\u6c28\u5316\u901f\u7387\u5e38\u6570\uff08h^{-1}\uff0c\u53d6\u503c 0.01 &#8211; 0.05\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(k_{n1}\uff1a\u785d\u5316\u7b2c\u4e00\u6b65\u901f\u7387\u5e38\u6570\uff08h^{-1}\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(k_{n2}(S)\uff1a\u785d\u5316\u7b2c\u4e8c\u6b65\u76d0\u5206\u4fee\u6b63\u901f\u7387\u5e38\u6570\uff08h^{-1}\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(S\uff1a\u571f\u58e4\u76d0\u5206\u6d53\u5ea6\uff08g\/L\uff09\\)<\/p>\n\n\n\n<p>2. &nbsp;\u690d\u7269\u6839\u7cfb\u5438\u6536\u6a21\u5757\uff08\u7c73\u6c0f\u65b9\u7a0b + \u76d0\u5206\u6291\u5236\uff09<\/p>\n\n\n\n<p>\u6839\u7cfb\u5438\u6536 NH_4 \u548c NO_3 \u7684\u901f\u7387\u9700\u52a0\u5165\u76d0\u5206\u6291\u5236\u56e0\u5b50 f(S)\uff0c\u4fee\u6b63\u540e\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p>\\(U_{NH_4} = V_{max_{NH_4}} \\cdot \\frac{NH_4}{K_{m_{NH_4}} + NH_4} \\cdot f(S)\\)<\/p>\n\n\n\n<p>\\(U_{NO_3} = V_{max_{NO_3}} \\cdot \\frac{NO_3}{K_{m_{NO_3}} + NO_3} \\cdot f(S)\\)<\/p>\n\n\n\n<p>\u5176\u4e2d\u76d0\u5206\u6291\u5236\u56e0\u5b50\uff1a<\/p>\n\n\n\n<p>\\(f(S) = \\frac{1}{1+(\\frac{S}{S_{50}})^n} \\)latex<\/p>\n\n\n\n<p>\u2022 \u53c2\u6570\u8bf4\u660e<\/p>\n\n\n\n<p>\u25e6 \\(V_{max_{NH_4}}\/V_{max_{NO_3}}\uff1aNH_4\/NO_3 \u6700\u5927\u5438\u6536\u901f\u7387\uff08mg\/cm^3\/h\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(K_{m_{NH_4}}\/K_{m_{NO_3}}\uff1a\u7c73\u6c0f\u5e38\u6570\uff08mg\/cm^3\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(S_{50} \\)\uff1a\u5438\u6536\u901f\u7387\u4e0b\u964d 50% \u65f6\u7684\u76d0\u5206\u6d53\u5ea6\uff08g\/L\uff09$<\/p>\n\n\n\n<p>\u25e6 \\(n \\)\uff1a\u6291\u5236\u66f2\u7ebf\u62df\u5408\u53c2\u6570<\/p>\n\n\n\n<p>3. &nbsp;\u6c2e\u7d20\u8fc1\u79fb\u6a21\u5757\uff08\u6269\u6563 &#8211; \u5bf9\u6d41\u65b9\u7a0b\uff0c\u76d0\u6e0d\u571f\u5b54\u9699\u4fee\u6b63\uff09<\/p>\n\n\n\n<p>\u6c2e\u7d20\u5728\u571f\u58e4\u4e2d\u7684\u8fc1\u79fb\u7531\u6269\u6563\u548c\u5bf9\u6d41\u5171\u540c\u9a71\u52a8\uff0c\u6269\u6563\u7cfb\u6570 D \u9700\u7ed3\u5408\u571f\u58e4\u542b\u6c34\u7387 \\theta \u548c\u76d0\u5206 S \u4fee\u6b63\uff1a<\/p>\n\n\n\n<p>\\(\\frac{\\partial N}{\\partial t} = D(\\theta,S) \\cdot \\frac{\\partial^2 N}{\\partial x^2} &#8211; v \\cdot \\frac{\\partial N}{\\partial x} \\)<\/p>\n\n\n\n<p>\u4fee\u6b63\u540e\u6269\u6563\u7cfb\u6570\uff1a<\/p>\n\n\n\n<p>\\(D(\\theta,S) = D_0 \\cdot \\theta^m \\cdot \\exp(-k_{salt} \\cdot S) \\)<\/p>\n\n\n\n<p>\u5bf9\u6d41\u901f\u7387\uff1a<\/p>\n\n\n\n<p>\\(v = \\frac{Q}{A \\cdot \\phi} \\)<\/p>\n\n\n\n<p>\u2022 \u53c2\u6570\u8bf4\u660e<\/p>\n\n\n\n<p>\u25e6\\( D_0\uff1a\u7eaf\u6c34\u4e2d\u6c2e\u7d20\u6269\u6563\u7cfb\u6570\uff08cm^2\/h\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(\\theta\uff1a\u571f\u58e4\u542b\u6c34\u7387\uff08\u76d0\u6e0d\u571f\u53d6\u503c 0.2 &#8211; 0.35\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(m\uff1a\u5b54\u9699\u8fde\u901a\u6027\u53c2\u6570\uff08\u53d6\u503c 2 &#8211; 3\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(k_{salt}\uff1a\u76d0\u5206\u5bf9\u6269\u6563\u7684\u5f71\u54cd\u7cfb\u6570\\)<\/p>\n\n\n\n<p>\u25e6 \\(Q\uff1a\u704c\u6e89\u6d41\u91cf\uff08cm^3\/h\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(A\uff1a\u571f\u58e4\u6a2a\u622a\u9762\u79ef\uff08cm^2\uff09\\)<\/p>\n\n\n\n<p>\u25e6 \\(\\phi\uff1a\u571f\u58e4\u5b54\u9699\u5ea6\\)<\/p>\n\n\n\n<p>4. &nbsp;\u6574\u5408\u5fae\u5206\u65b9\u7a0b<\/p>\n\n\n\n<p>\\(\u7efc\u5408\u8f6c\u5316\u3001\u5438\u6536\u3001\u8fc1\u79fb\u8fc7\u7a0b\uff0cNH_4 \u548c NO_3 \u7684\u65f6\u7a7a\u53d8\u5316\u65b9\u7a0b\uff1a\\)<\/p>\n\n\n\n<p>\\(\\frac{\\partial NH_4}{\\partial t} = k_{amm}OrgN &#8211; k_{n1}NH_4 &#8211; U_{NH_4} + D(\\theta,S)\\frac{\\partial^2 NH_4}{\\partial x^2} &#8211; v\\frac{\\partial NH_4}{\\partial x} \\)<\/p>\n\n\n\n<p>\\(\\frac{\\partial NO_3}{\\partial t} = k_{n1}NH_4 &#8211; k_{n2}(S)NO_3 &#8211; U_{NO_3} + D(\\theta,S)\\frac{\\partial^2 NO_3}{\\partial x^2} &#8211; v\\frac{\\partial NO_3}{\\partial x} \\)<\/p>\n\n\n\n<p>\u4e8c\u3001 MATLAB \u521d\u6b65\u4ee3\u7801\u6846\u67b6\uff08\u53c2\u6570\u7528\u7b26\u53f7\u8868\u793a\uff09<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>% -------------------------- 1. \u5b9a\u4e49\u6a21\u578b\u53c2\u6570 --------------------------\n\nk_amm = 0.02; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u6c28\u5316\u901f\u7387\u5e38\u6570 h^-1\n\nk_n1 = 0.015; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u785d\u5316\u7b2c\u4e00\u6b65\u901f\u7387\u5e38\u6570 h^-1\n\nVmax_NH4 = 5; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% NH4\u6700\u5927\u5438\u6536\u901f\u7387 mg\/cm^3\/h\n\nKm_NH4 = 2; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% NH4\u7c73\u6c0f\u5e38\u6570 mg\/cm^3\n\nVmax_NO3 = 4; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% NO3\u6700\u5927\u5438\u6536\u901f\u7387 mg\/cm^3\/h\n\nKm_NO3 = 1.5; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% NO3\u7c73\u6c0f\u5e38\u6570 mg\/cm^3\n\nS50 = 8; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u76d0\u5206\u534a\u6291\u5236\u6d53\u5ea6 g\/L\n\nn = 2; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u6291\u5236\u66f2\u7ebf\u53c2\u6570\n\nD0 = 1e-5; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u7eaf\u6c34\u6269\u6563\u7cfb\u6570 cm^2\/h\n\nm = 2.5; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u5b54\u9699\u8fde\u901a\u6027\u53c2\u6570\n\nk_salt = 0.1; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u76d0\u5206\u6269\u6563\u5f71\u54cd\u7cfb\u6570\n\nQ = 0.5; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u704c\u6e89\u6d41\u91cf cm^3\/h\n\nA = 10; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u571f\u58e4\u6a2a\u622a\u9762\u79ef cm^2\n\nphi = 0.4; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u571f\u58e4\u5b54\u9699\u5ea6\n\nS = 5; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u521d\u59cb\u76d0\u5206\u6d53\u5ea6 g\/L\n\ntheta = 0.3; \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0% \u571f\u58e4\u542b\u6c34\u7387\n\nx = linspace(0,20,100); % \u571f\u58e4\u6df1\u5ea6\u7f51\u683c 0-20cm\uff0c100\u4e2a\u8282\u70b9\n\nt = linspace(0,100,50); % \u65f6\u95f4\u7f51\u683c 0-100h\uff0c50\u4e2a\u65f6\u95f4\u70b9\n\n% -------------------------- 2. \u5b9a\u4e49\u4fee\u6b63\u51fd\u6570 --------------------------\n\n% \u76d0\u5206\u5bf9\u6839\u7cfb\u5438\u6536\u7684\u6291\u5236\u56e0\u5b50\n\nf_S = @(S) 1.\/(1 + (S\/S50).^n);\n\n% \u76d0\u5206\u548c\u542b\u6c34\u7387\u4fee\u6b63\u7684\u6269\u6563\u7cfb\u6570\n\nD = @(theta,S) D0 * theta^m * exp(-k_salt * S);\n\n% \u785d\u5316\u7b2c\u4e8c\u6b65\u76d0\u5206\u4fee\u6b63\u901f\u7387\u5e38\u6570\n\nk_n2 = @(S) (39.59*(log(S)).^2 - 244.27*log(S) + 393.86)*1e-3;\n\n% \u5bf9\u6d41\u901f\u7387\n\nv = Q\/(A * phi);\n\n% -------------------------- 3. \u5b9a\u4e49\u504f\u5fae\u5206\u65b9\u7a0b --------------------------\n\n% \u8c03\u7528pdepe\u51fd\u6570\u6c42\u89e3\uff0c\u9700\u5b9a\u4e49\u4e09\u4e2a\u5b50\u51fd\u6570\uff1apdefun, icfun, bcfun\n\nm_pde = 0; \u00a0% \u5750\u6807\u7cfb\u53c2\u6570\uff080=\u76f4\u89d2\u5750\u6807\u7cfb\uff09\n\nsol = pdepe(m_pde, @pdefun, @icfun, @bcfun, x, t);\n\n% \u63d0\u53d6\u7ed3\u679c\uff1asol(:,:,1)=OrgN, sol(:,:,2)=NH4, sol(:,:,3)=NO3\n\nOrgN = sol(:,:,1);\n\nNH4 = sol(:,:,2);\n\nNO3 = sol(:,:,3);\n\n% -------------------------- 4. \u5b9a\u4e49PDE\u65b9\u7a0b\u51fd\u6570 --------------------------\n\nfunction &#091;c,f,s] = pdefun(x,t,u,DuDx)\n\n\u00a0\u00a0\u00a0\u00a0% u = &#091;OrgN; NH4; NO3]; DuDx = d(u)\/dx\n\n\u00a0\u00a0\u00a0\u00a0OrgN = u(1); NH4 = u(2); NO3 = u(3);\n\n\u00a0\u00a0\u00a0\u00a0dOrgNdx = DuDx(1); dNH4dx = DuDx(2); dNO3dx = DuDx(3);\n\n\u00a0\u00a0\u00a0\u00a0% \u8c03\u7528\u5916\u90e8\u53c2\u6570\n\n\u00a0\u00a0\u00a0\u00a0global k_amm k_n1 k_n2 Vmax_NH4 Km_NH4 Vmax_NO3 Km_NO3 f_S D v S theta\n\n\u00a0\u00a0\u00a0\u00a0% \u6839\u7cfb\u5438\u6536\u901f\u7387\n\n\u00a0\u00a0\u00a0\u00a0U_NH4 = Vmax_NH4 * NH4\/(Km_NH4 + NH4) * f_S(S);\n\n\u00a0\u00a0\u00a0\u00a0U_NO3 = Vmax_NO3 * NO3\/(Km_NO3 + NO3) * f_S(S);\n\n\u00a0\u00a0\u00a0\u00a0% \u65b9\u7a0b\u7cfb\u6570 c*du\/dt = d\/dx(f) + s\n\n\u00a0\u00a0\u00a0\u00a0c = &#091;1; 1; 1];\n\n\u00a0\u00a0\u00a0\u00a0f = &#091;0; D(theta,S)*dNH4dx; D(theta,S)*dNO3dx] - &#091;0; v*NH4; v*NO3];\n\n\u00a0\u00a0\u00a0\u00a0s = &#091;-k_amm*OrgN;\n\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0k_amm*OrgN - k_n1*NH4 - U_NH4;\n\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0k_n1*NH4 - k_n2(S)*NO3 - U_NO3];\n\nend\n\n% -------------------------- 5. \u5b9a\u4e49\u521d\u59cb\u6761\u4ef6\u51fd\u6570 --------------------------\n\nfunction u0 = icfun(x)\n\n\u00a0\u00a0\u00a0\u00a0% \u521d\u59cb\u571f\u58e4\u6c2e\u7d20\u5206\u5e03\uff1a\u8868\u5c42\u6709\u673a\u6c2e\u591a\uff0c\u6df1\u5c42\u5c11\uff1bNH4\u3001NO3\u521d\u59cb\u6d53\u5ea6\u4f4e\n\n\u00a0\u00a0\u00a0\u00a0if x &lt; 5\n\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0u0 = &#091;10; 0.5; 0.3]; % OrgN=10, NH4=0.5, NO3=0.3 mg\/cm^3\n\n\u00a0\u00a0\u00a0\u00a0else\n\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0u0 = &#091;2; 0.1; 0.1]; \u00a0% \u6df1\u5c42\u6c2e\u7d20\u6d53\u5ea6\n\n\u00a0\u00a0\u00a0\u00a0end\n\nend\n\n% -------------------------- 6. \u5b9a\u4e49\u8fb9\u754c\u6761\u4ef6\u51fd\u6570 --------------------------\n\nfunction &#091;pl,ql,pr,qr] = bcfun(xl,ul,xr,ur,t)\n\n\u00a0\u00a0\u00a0\u00a0% \u5de6\u8fb9\u754c\uff08\u5730\u8868x=0\uff09\uff1a\u704c\u6e89\u8f93\u5165\uff0c\u6c2e\u7d20\u901a\u91cf\u56fa\u5b9a\n\n\u00a0\u00a0\u00a0\u00a0pl = &#091;5 - ul(1); 0.2 - ul(2); 0.1 - ul(3)];\n\n\u00a0\u00a0\u00a0\u00a0ql = &#091;0; 0; 0];\n\n\u00a0\u00a0\u00a0\u00a0% \u53f3\u8fb9\u754c\uff08\u6df1\u5c42x=20cm\uff09\uff1a\u96f6\u901a\u91cf\uff0c\u6c2e\u7d20\u4e0d\u6d41\u5931\n\n\u00a0\u00a0\u00a0\u00a0pr = &#091;0; 0; 0];\n\n\u00a0\u00a0\u00a0\u00a0qr = &#091;1; 1; 1];\n\nend\n\n% -------------------------- 7. \u7ed3\u679c\u53ef\u89c6\u5316 --------------------------\n\nfigure;\n\nsubplot(3,1,1);\n\nsurf(x,t,OrgN); xlabel('\u571f\u58e4\u6df1\u5ea6\/cm'); ylabel('\u65f6\u95f4\/h'); zlabel('\u6709\u673a\u6c2e\u6d53\u5ea6 mg\/cm^3'); title('\u6709\u673a\u6c2e\u65f6\u7a7a\u5206\u5e03');\n\nsubplot(3,1,2);\n\nsurf(x,t,NH4); xlabel('\u571f\u58e4\u6df1\u5ea6\/cm'); ylabel('\u65f6\u95f4\/h'); zlabel('NH4\u6d53\u5ea6 mg\/cm^3'); title('\u94f5\u6001\u6c2e\u65f6\u7a7a\u5206\u5e03');\n\nsubplot(3,1,3);\n\nsurf(x,t,NO3); xlabel('\u571f\u58e4\u6df1\u5ea6\/cm'); ylabel('\u65f6\u95f4\/h'); zlabel('NO3\u6d53\u5ea6 mg\/cm^3'); title('\u785d\u6001\u6c2e\u65f6\u7a7a\u5206\u5e03');<\/code><\/pre>\n\n\n\n<p>\u4e09\u3001 \u8c03\u8bd5\u4e0e\u4f18\u5316\u5efa\u8bae<\/p>\n\n\n\n<p>1. \u53c2\u6570\u66ff\u6362\uff1a\u5c06\u4ee3\u7801\u4e2d\u7b26\u53f7\u53c2\u6570\u66ff\u6362\u4e3a\u76ee\u6807\u571f\u58e4\uff08\u5982\u76d0\u6e0d\u571f\uff09\u7684\u5b9e\u6d4b\u503c\u6216\u6587\u732e\u503c\uff0c\u63d0\u5347\u6a21\u62df\u51c6\u786e\u6027\u3002<\/p>\n\n\n\n<p>2. \u7a7a\u95f4\u5bfc\u6570\u79bb\u6563\uff1a\u82e5\u4f7f\u7528 ode45 \u6c42\u89e3\uff0c\u9700\u7528\u6709\u9650\u5dee\u5206\u6cd5\u5c06\u4e8c\u9636\u7a7a\u95f4\u5bfc\u6570 \\(\\frac{\\partial^2 N}{\\partial x^2} \\)\u79bb\u6563\u4e3a\u77e9\u9635\u5f62\u5f0f\u3002<\/p>\n\n\n\n<p>3. \u76d0\u5206\u68af\u5ea6\u6d4b\u8bd5\uff1a\u8c03\u6574 S \u7684\u53d6\u503c\u8303\u56f4\uff080 &#8211; 15 g\/L\uff09\uff0c\u89c2\u5bdf\u76d0\u5206\u5bf9\u785d\u5316\u901f\u7387\u548c\u6839\u7cfb\u5438\u6536\u7684\u6291\u5236\u6548\u5e94\u3002<\/p>\n\n\n\n<p>4. \u53ef\u89c6\u5316\u4f18\u5316\uff1a\u53ef\u4f7f\u7528 animatedline \u51fd\u6570\u5236\u4f5c\u6c2e\u7d20\u6d53\u5ea6\u968f\u65f6\u95f4\u53d8\u5316\u7684\u52a8\u6001\u66f2\u7ebf\uff0c\u66f4\u76f4\u89c2\u5c55\u793a\u8fc1\u79fb\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p>\u6211\u53ef\u4ee5\u5e2e\u4f60\u6574\u7406\u4ee3\u7801\u8c03\u8bd5\u7684\u5e38\u89c1\u95ee\u9898\u53ca\u89e3\u51b3\u65b9\u6cd5\uff0c\u9700\u8981\u5417\uff1f<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u690d\u7269\u6c2e\u7d20\u5438\u6536\u53ca\u571f\u58e4\u6c2e\u7d20\u8f6c\u5316\u8fc1\u79fb MATLAB \u6a21\u62df\u65b9\u6848\uff08\u6574\u5408\u7248\uff09 \u4e00\u3001 \u6a21\u578b\u6838\u5fc3 &hellip; <a href=\"http:\/\/www.ex-5.com\/?p=35\">\u7ee7\u7eed\u9605\u8bfb <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/www.ex-5.com\/index.php?rest_route=\/wp\/v2\/posts\/35"}],"collection":[{"href":"http:\/\/www.ex-5.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.ex-5.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.ex-5.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.ex-5.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=35"}],"version-history":[{"count":16,"href":"http:\/\/www.ex-5.com\/index.php?rest_route=\/wp\/v2\/posts\/35\/revisions"}],"predecessor-version":[{"id":51,"href":"http:\/\/www.ex-5.com\/index.php?rest_route=\/wp\/v2\/posts\/35\/revisions\/51"}],"wp:attachment":[{"href":"http:\/\/www.ex-5.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=35"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.ex-5.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=35"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.ex-5.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}