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½ð³æ (СÓÐÃûÆø)

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MatlabС°×£¬¼±Ðè¼ÆËãÒ»¸öÄ£ÐÍ£¬½â΢·Ö·½³Ì×飬Ç󶮵ĴóÉñ¿´¿´ÔõôÐ޸ġ£Íò·Ö¸Ðл
function dy = funct(t,y)

I = 50 % mA
F = 96487 % C/mol
c0 = 10 % mM
Vol = 3.344 % ml
Q = 6.5 % ml/min
A = 33.75 % cm2

syms x
eqn = 0.86*x+0.4*(x*exp(-asinh(theta/(-2*x)))+x*exp(asinh(theta/(-2*x))))==y(3)
cma = double(solve(eqn,x))

cmion = (y(3)-0.86*cma)/0.4

phi_sp = asinh(-3/y(2))
phi_ele = asinh(-3/cma)

phi_mem = (I*170)/(-1.12*F*(cma.*cosh(phi_ele)+y(2).*cosh(phi_sp)))

J = -(1.12*1e-3/170)*(2*cma.*cosh(phi_ele)-2*y(2).*cosh(phi_sp))+3*phi_mem

dy=zeros(3,1);
dy(1) = (1e4*I/A)/(116*F)

dy(2) = -J/(250e-6*0.5)+(c0-y(2))/(0.5*(Vol/Q)*60)

dy(3)  = J/(290*1e-6)

end
clear all;
c0=10
tspan=[0 600]
[t,y] = ode45(@funct,tspan,[0 c0 1.66*c0])

plot(t, y(:,2))
xlabel('t'),ylabel('c')

´íÎóʹÓà odearguments (line 92)
FUNCT ·µ»ØµÄʸÁ¿µÄ³¤¶ÈΪ 2£¬µ«³õʼÌõ¼þʸÁ¿µÄ³¤¶ÈΪ 3¡£FUNCT ·µ»ØµÄʸÁ¿ºÍ³õʼÌõ¼þʸÁ¿µÄÔªËØÊýÄ¿±ØÐëÏàͬ¡£

³ö´í ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...
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chendequan

Ìú³æ (СÓÐÃûÆø)

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thetaֵδ֪£¬eqn·½³ÌÇó½âcma¿ÉÄÜ»áÓöµ½ÎÞ½âÇé¿ö£¬½¨ÒéÌṩ¹«Ê½×ÊÁÏ¿´¿´

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2Â¥2019-06-23 10:06:51
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½ò½ò°®Ë¯¾õ

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
2Â¥: Originally posted by chendequan at 2019-06-23 10:06:51
thetaֵδ֪£¬eqn·½³ÌÇó½âcma¿ÉÄÜ»áÓöµ½ÎÞ½âÇé¿ö£¬½¨ÒéÌṩ¹«Ê½×ÊÁÏ¿´¿´

function dydt = funct(t,x, y)

I = 50; % mA
F = 96487; % C/mol
c0 = 10; % mM
Vol = 3.344; % ml
Q = 6.5; % ml/min
A = 33.75; % cm2
y1=y(1); y2=y(2); y3=y(3);
y3 = 0.86*x+0.4*(x*exp(-asinh(y1/(-2*x)))+x*exp(asinh(y1/(-2*x))))

phi_sp = asinh(-3/y2)
phi_ele = asinh(-3/x)

phi_mem=(I*170)/(-1.12*F*(x*cosh(phi_ele)+y2*cosh(phi_sp)))

J =-(1.12*1e-3/170)*(2*x*cosh(phi_ele)-2*y2*cosh(phi_sp))+3*phi_mem

dy1dt = (1e4*I/A)/(116*F)

dy2dt = -J/(250e-6*0.5)+(c0-y2)/(0.5*(Vol/Q)*60)

dy3dt = J/(290*1e-6)

end
clear all;
I = 50; % mA
F = 96487; % C/mol
c0 = 10; % mM
Vol = 3.344; % ml
Q = 6.5; % ml/min
A = 33.75; % cm2
tspan=[0 600]
x0=c0

[t,x,y] = ode45(@funct,tspan, c0, [0 c0 1.66*c0])

plot(t, theta)
xlabel('t'),ylabel('c')

³ö´í ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

¸ÄÁ˳ÌÐò£¬ÏÖÔÚ´íÎó±ä³ÉÕâÑù¡£¹«Ê½¾ÍÊÇÏë½âÒ»¸öÈý¸öδ֪ÊýµÄ΢·Ö·½³Ì×飬µ«ÊÇÀïÃæÓÐδ֪Êý
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3Â¥2019-06-23 20:57:24
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½ò½ò°®Ë¯¾õ

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
2Â¥: Originally posted by chendequan at 2019-06-23 10:06:51
thetaֵδ֪£¬eqn·½³ÌÇó½âcma¿ÉÄÜ»áÓöµ½ÎÞ½âÇé¿ö£¬½¨ÒéÌṩ¹«Ê½×ÊÁÏ¿´¿´

function dydt = funct(t,x, y)

I = 50; % mA
F = 96487; % C/mol
c0 = 10; % mM
Vol = 3.344; % ml
Q = 6.5; % ml/min
A = 33.75; % cm2
y1=y(1); y2=y(2); y3=y(3);
y3 = 0.86*x+0.4*(x*exp(-asinh(y1/(-2*x)))+x*exp(asinh(y1/(-2*x))))

phi_sp = asinh(-3/y2)
phi_ele = asinh(-3/x)

phi_mem=(I*170)/(-1.12*F*(x*cosh(phi_ele)+y2*cosh(phi_sp)))

J =-(1.12*1e-3/170)*(2*x*cosh(phi_ele)-2*y2*cosh(phi_sp))+3*phi_mem

dy1dt = (1e4*I/A)/(116*F)

dy2dt = -J/(250e-6*0.5)+(c0-y2)/(0.5*(Vol/Q)*60)

dy3dt = J/(290*1e-6)

end
clear all;
I = 50; % mA
F = 96487; % C/mol
c0 = 10; % mM
Vol = 3.344; % ml
Q = 6.5; % ml/min
A = 33.75; % cm2
tspan=[0 600]
x0=c0

[t,x,y] = ode45(@funct,tspan, c0, [0 c0 1.66*c0])

plot(t, theta)
xlabel('t'),ylabel('c')

³ö´í ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

¸ÄÁ˳ÌÐò£¬ÏÖÔÚ´íÎó±ä³ÉÕâÑù¡£¹«Ê½¾ÍÊÇÏë½âÒ»¸öÈý¸öδ֪ÊýµÄ΢·Ö·½³Ì×飬µ«ÊÇÀïÃæÓÐδ֪Êý
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4Â¥2019-06-23 20:57:30
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½ò½ò°®Ë¯¾õ

½ð³æ (СÓÐÃûÆø)

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ÒýÓûØÌû:
2Â¥: Originally posted by chendequan at 2019-06-23 10:06:51
thetaֵδ֪£¬eqn·½³ÌÇó½âcma¿ÉÄÜ»áÓöµ½ÎÞ½âÇé¿ö£¬½¨ÒéÌṩ¹«Ê½×ÊÁÏ¿´¿´

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5Â¥2019-06-23 20:58:43
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hzlhm

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7Â¥2019-06-24 13:20:05
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chendequan

Ìú³æ (СÓÐÃûÆø)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

ÒýÓûØÌû:
5Â¥: Originally posted by ½ò½ò°®Ë¯¾õ at 2019-06-23 20:58:43
·Ç³£¸Ðл£¬Äܰïæ½â¾ö±ØÓÐÖØÐ»...

¸öÈËÇ©ÃûÀïÃæÓÐÎÒÁªÏµ·½Ê½£¬ÎÊÌâ×ÊÁÏÒªÆëÈ«£¬ÒªÇóÒª¾ßÌåÏêϸ£¬ÕâÑù±ãÓÚÎÊÌ⼰ʱ½â¾ö¡£
QQ£º516477448£¬ÕæÐİïÖú½â¾öMATLABÏà¹ØÎÊÌ⣬ÌṩÏêϸ×ÊÁÏ£¬WordÎĵµÃ÷È·¾ßÌåÎÊÌâ¼°ÒªÇ󣬾¡Á¦¶øÎª£¡
8Â¥2019-06-24 15:28:52
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½ò½ò°®Ë¯¾õ

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
7Â¥: Originally posted by hzlhm at 2019-06-24 13:20:05
½¨ÒéÄ㣬°Ñ¾ßÌåµÄ΢·Ö·½³Ì×éºÍÌõ¼þÌù³öÀ´¿´Ò»¿´¡£ÕâÑù¾Í¿ÉÒÔ¼õÉÙһЩäĿÐÔ¡£

dy(1)=a*y(1)+b*y(2);
y(2)=c*y(1)+d*y(3);
dy(3)=-e*y(2)*(y(3)-t)/y(1);

function daedi
a=-0.2; b=0.5; c=0.1; d=-1; e=0.3;
y0=[0.8;0.5;0.1]; %³õÖµ£¬y0(2)=0.5ÊDz²âÖµ
options=optimset('display','off');
y0(2)=fsolve(@(y2)y2-(c*y0(1)+d*y0(3)),y0(2),options); %Çó³öÏàÈݵijõÖµy0(2)
% Çó½â΢·Ö·½³Ì
[t,y]=ode45(@(t,y)myodefun(t,y,a,b,c,d,e),[0,20],y0);
figure('numbertitle','off','name','DAE Çó½âʾÀý ·½·¨1.2')
plot(t,y)
legend('y1(t)','y2(t)','y3(t)')

function dy=myodefun(t,y,a,b,c,d,e)
dy=zeros(3,1); % dy(2)=0ºÜÖØÒª£¬·ñÔò·´Çó³öy(2)ºó»á±»»ý·Ö
% ÏÈÇó½â´úÊý·½³Ì£¬Ë³ÐòºÜÖØÒª
cons=@(y2)y2-(c*y(1)+d*y(3)); % Òþʽ´úÊýÔ¼Êø
options=optimset('display','off'); % ¹Ø±ÕÌáʾ
y(2)=fsolve(cons,y(2),options); %ÓÃÉϴεÄy(2)×÷Ϊ²Â²âÖµ
dy(1)=a*y(1)+b*y(2);
dy(3)=-e*y(2)*(y(3)-t)/y(1);
ÏÖÔÚͨ¹ýÕâ¸öÀý×ÓÒѾ­¿ÉÒÔÔËÐУ¬ÏëÎÊÄúÔõô¼ÌÐø±àдÕâ¸öÀý×ÓÖÐy(2)ËætµÄ¶¯Ì¬±ä»¯ÄØ
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9Â¥2019-06-28 04:59:55
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½ò½ò°®Ë¯¾õ

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
8Â¥: Originally posted by chendequan at 2019-06-24 15:28:52
¸öÈËÇ©ÃûÀïÃæÓÐÎÒÁªÏµ·½Ê½£¬ÎÊÌâ×ÊÁÏÒªÆëÈ«£¬ÒªÇóÒª¾ßÌåÏêϸ£¬ÕâÑù±ãÓÚÎÊÌ⼰ʱ½â¾ö¡£...

dy(1)=a*y(1)+b*y(2);
y(2)=c*y(1)+d*y(3);
dy(3)=-e*y(2)*(y(3)-t)/y(1);

function daedi
a=-0.2; b=0.5; c=0.1; d=-1; e=0.3;
y0=[0.8;0.5;0.1]; %³õÖµ£¬y0(2)=0.5ÊDz²âÖµ
options=optimset('display','off');
y0(2)=fsolve(@(y2)y2-(c*y0(1)+d*y0(3)),y0(2),options); %Çó³öÏàÈݵijõÖµy0(2)
% Çó½â΢·Ö·½³Ì
[t,y]=ode45(@(t,y)myodefun(t,y,a,b,c,d,e),[0,20],y0);
figure('numbertitle','off','name','DAE Çó½âʾÀý ·½·¨1.2')
plot(t,y)
legend('y1(t)','y2(t)','y3(t)')

function dy=myodefun(t,y,a,b,c,d,e)
dy=zeros(3,1); % dy(2)=0ºÜÖØÒª£¬·ñÔò·´Çó³öy(2)ºó»á±»»ý·Ö
% ÏÈÇó½â´úÊý·½³Ì£¬Ë³ÐòºÜÖØÒª
cons=@(y2)y2-(c*y(1)+d*y(3)); % Òþʽ´úÊýÔ¼Êø
options=optimset('display','off'); % ¹Ø±ÕÌáʾ
y(2)=fsolve(cons,y(2),options); %ÓÃÉϴεÄy(2)×÷Ϊ²Â²âÖµ
dy(1)=a*y(1)+b*y(2);
dy(3)=-e*y(2)*(y(3)-t)/y(1);
ÏÖÔÚͨ¹ýÕâ¸öÀý×ÓÒѾ­¿ÉÒÔÔËÐУ¬ÏëÎÊÄúÔõô¼ÌÐø±àдÕâ¸öÀý×ÓÖÐy(2)ËætµÄ¶¯Ì¬±ä»¯ÄØ
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