Can the equations in the differential equation group be represented by symbols when matlab ode solves the differential equation group ?

Question

Hou X.Y 2022-3-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1676554-can-the-equations-in-the-differential-equation-group-be-represented-by-symbols-when-matlab-ode-solve

评论： Torsten 2022-3-22

main function:

function dcdzh2h2sco2_centri = dcdzh2h2sco2_centri(z,c)
R = 8.314;
g = 1000;
Mi_h2s = 34;
Mi_co2 = 44;
Mi_ch4 = 16;
syms T z c_ch4 c_co2 c_h2s dc_31 dc_32 dc_33
Tz = 293 + 10*z;
alpha_1_2 = log((3.6029/(1.3932))*((c_co2)/c_h2s))/(log(Tz/293.15));
alpha_1_3 = log((3.6029/(37.063))*((c_ch4)/c_h2s))/(log(Tz/293.15));
alpha_2_3 = log((1.3932/(37.063))*((c_ch4)/c_co2))/(log(Tz/293.15));
alpha_h2sT = (c_co2/(c_ch4+c_co2+c_h2s))*(-alpha_1_2)+((c_ch4)/(c_ch4+c_co2+c_h2s))*(-alpha_1_3);
alpha_co2T = (c_ch4/(c_ch4+c_co2+c_h2s))*(-alpha_2_3)+((c_h2s)/(c_ch4+c_co2+c_h2s))*(alpha_1_2);
alpha_ch4T = (c_h2s/(c_ch4+c_co2+c_h2s))*(alpha_1_3)+((c_co2)/(c_ch4+c_co2+c_h2s))*(alpha_2_3);
alpha_h2s = subs(alpha_h2sT,T,Tz);
alpha_co2 = subs(alpha_co2T,T,Tz);
alpha_ch4 = subs(alpha_ch4T,T,Tz);
Hi_h2s = 1/((Mi_h2s*g)/(R*Tz));
Hi_co2 = 1/((Mi_co2*g)/(R*Tz));
Hi_ch4 = 1/((Mi_ch4*g)/(R*Tz));
dcdz_h2s_1 = -(0.027*((1 + alpha_h2s)/Tz)-(1/Hi_h2s))
dcdz_co2_1 = (-(0.027*((1 + alpha_co2)/Tz)-(1/Hi_co2)))
dcdz_ch4_1 = (-(0.027*((1 + alpha_ch4)/Tz)-(1/Hi_ch4)))
dc_11 = char(dcdz_h2s_1)
dc_12 = char(dcdz_co2_1)
dc_13 = char(dcdz_ch4_1)
dc_21 = strrep(dc_11,'c_h2s','c(1)');
dc_21 = strrep(dc_21,'c_co2','c(2)');
dc_21 = strrep(dc_21,'c_ch4','c(3)')
dc_22 = strrep(dc_12,'c_h2s','c(1)');
dc_22 = strrep(dc_22,'c_co2','c(2)');
dc_22 = strrep(dc_22,'c_ch4','c(3)')
dc_23 = strrep(dc_13,'c_h2s','c(1)');
dc_23 = strrep(dc_23,'c_co2','c(2)');
dc_23 = strrep(dc_23,'c_ch4','c(3)')
dc_31 = str2sym(dc_21)
dc_32 = str2sym(dc_22)
dc_33 = str2sym(dc_23)
dcdzh2h2sco2_centri = zeros(3,1);
dcdzh2h2sco2_centri = [dc_31;dc_32;dc_33]
end

and solve it:

[z,c] = ode45(@dcdzh2h2sco2_centri,[0:0.1:100],[3.6029 1.3932 37.063])

it gives results and errors as following:

dcdzh2h2sco2_centri =

((27*c(3)*log((7004729934415739*c(3))/(72057594037927936*c(1))))/(log((200*z)/5863 + 5860/5863)*(c(1) + c(2) + c(3))) + (27*c(2)*log((36029*c(2))/(13932*c(1))))/(log((200*z)/5863 + 5860/5863)*(c(1) + c(2) + c(3))) - 27)/(10000*z + 293000) + 1/((4157*z)/1700000 + 1218001/17000000)

1/((4157*z)/2200000 + 1218001/22000000) - ((27*c(1)*log((36029*c(2))/(13932*c(1))))/(log((200*z)/5863 + 5860/5863)*(c(1) + c(2) + c(3))) - (27*c(3)*log((5417297035514729*c(3))/(144115188075855872*c(2))))/(log((200*z)/5863 + 5860/5863)*(c(1) + c(2) + c(3))) + 27)/(10000*z + 293000)

1/((4157*z)/800000 + 1218001/8000000) - ((27*c(2)*log((5417297035514729*c(3))/(144115188075855872*c(2))))/(log((200*z)/5863 + 5860/5863)*(c(1) + c(2) + c(3))) + (27*c(1)*log((7004729934415739*c(3))/(72057594037927936*c(1))))/(log((200*z)/5863 + 5860/5863)*(c(1) + c(2) + c(3))) + 27)/(10000*z + 293000)

Error using odearguments ( line 113 )

Input must be single precision or double precision floating point value.

I want to use the symbols deducing results to represent diffenrential equation in the differential equation groups,could you help me?Thanks a lot.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Torsten 2022-3-21

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1676554-can-the-equations-in-the-differential-equation-group-be-represented-by-symbols-when-matlab-ode-solve#answer_923179

function dcdzh2h2sco2_centri = dcdzh2h2sco2_centri(z,c)  
R = 8.314;
g = 1000;
Mi_h2s = 34;
Mi_co2 = 44;
Mi_ch4 = 16;
syms T z c_ch4 c_co2 c_h2s dc_31 dc_32 dc_33 Z
Tz = 293 + 10*z;
alpha_1_2 = log((3.6029/(1.3932))*((c_co2)/c_h2s))/(log(Tz/293.15));
alpha_1_3 = log((3.6029/(37.063))*((c_ch4)/c_h2s))/(log(Tz/293.15));
alpha_2_3 = log((1.3932/(37.063))*((c_ch4)/c_co2))/(log(Tz/293.15));
alpha_h2sT = (c_co2/(c_ch4+c_co2+c_h2s))*(-alpha_1_2)+((c_ch4)/(c_ch4+c_co2+c_h2s))*(-alpha_1_3);
alpha_co2T = (c_ch4/(c_ch4+c_co2+c_h2s))*(-alpha_2_3)+((c_h2s)/(c_ch4+c_co2+c_h2s))*(alpha_1_2);
alpha_ch4T = (c_h2s/(c_ch4+c_co2+c_h2s))*(alpha_1_3)+((c_co2)/(c_ch4+c_co2+c_h2s))*(alpha_2_3);
alpha_h2s = subs(alpha_h2sT,T,Tz);
alpha_co2 = subs(alpha_co2T,T,Tz);
alpha_ch4 = subs(alpha_ch4T,T,Tz);
Hi_h2s = 1/((Mi_h2s*g)/(R*Tz));
Hi_co2 = 1/((Mi_co2*g)/(R*Tz));
Hi_ch4 = 1/((Mi_ch4*g)/(R*Tz));
dcdz_h2s_1 = -(0.027*((1 + alpha_h2s)/Tz)-(1/Hi_h2s));
dcdz_co2_1 = (-(0.027*((1 + alpha_co2)/Tz)-(1/Hi_co2)));
dcdz_ch4_1 = (-(0.027*((1 + alpha_ch4)/Tz)-(1/Hi_ch4)));
f = matlabFunction([dcdz_h2s_1;dcdz_co2_1;dcdz_ch4_1]);
dcdzh2h2sco2_centri = f(c(3),c(2),c(1),z);
end

Doublecheck whether the order of the arguments for f is correct, i.e. look if f has the form

@(c_ch4, c_co2, c_h2s, z) [f1;f2;f3]

(I guess c_ch4 corresponds to c(3), c_co2 corresponds to c(2) and c_h2s corresponds to c(1) in your code)

4 个评论
显示 2更早的评论隐藏 2更早的评论

Hou X.Y 2022-3-22

Thank you very much.It does work!

Torsten 2022-3-22

My pleasure.

请先登录，再进行评论。

Answer 2

John D'Errico 2022-3-21

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1676554-can-the-equations-in-the-differential-equation-group-be-represented-by-symbols-when-matlab-ode-solve#answer_923104

编辑：John D'Errico 2022-3-21

Sorry, but the numerical ode solvers, such as ODE45 are NOT symbolic tools. They CANNOT solve an ode with symbolic parameters. Period.

If you want to solve an ode using symbolic parameters then you would need to use a tool like DSOLVE. Of course, there is no assurance a symbolic solution can be found. It would be my guess that most such complicated odes will fail in that respect, lacking any symbolic solution, but you may always get lucky.

Such is life in the big city. There are many things in life we may want, but cannot have.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Hou X.Y 2022-3-21

编辑：Hou X.Y 2022-3-21

Thanks for your answer.But it seems that you have a wrong understanding of my question:what I want is not use ode to get symbols solution,I want to let the symbols(eg.dc_31) represent the results of symbolic operation,then let them represent the equations in a differential equation group,then use ode to solve it and get numerical solution.

请先登录，再进行评论。