Explicit solution could not be found.

Question

mohamed elkasemy 2021-11-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1579324-explicit-solution-could-not-be-found

回答： Walter Roberson 2021-11-4

clc;
clear all; 
close all;
syms y1(t) y2(t) y3(t) y4(t) y5(t) y6(t) y7(t) y8(t) 
C = 3*10^10;
KT = 0.086173324;  % MeV
M0 = 1.0078;       % u
M1 = 1.0078;       % u
M2 = 2.014102;     % u
M3 = 1.0078;       % u
M4 = 2.014102;     % u
M5 = 2.014102;     % u
M6 = 3.016030;     % u
M7 = 2.014102;     % u
M8 = 3.016030;     % u
M9 = 3.016030;     % u
M10 = 3.016030;    % u
M11 = 4.002603;    % u
Z0 = 1;  
Z1 = 1;  
Z2 = 1;  
Z3 = 1;
Z4 = 1;  
Z5 = 1;  
Z6 = 2;  
Z7 = 1;
Z8 = 2;  
Z9 = 2;
Z10 = 2;
Z11 = 2;
Eat = 0.98951013;
m01 = (M0*M1)/(M0+M1);
m23 = (M2*M3)/(M2+M3);
m45 = (M4*M5)/(M4+M5);
m67 = (M6*M7)/(M6+M7);
m89 = (M8*M9)/(M8+M9);
m1011 = (M10*M11)/(M10+M11);
cont = (931.494)./(3*10^10)^2;
cont1 = 10^-24;
sy0 = 0.1; 
Q2 = (4.08*10^-15)*((y8./KT)^(-2/3))*exp(-3.381*((y8./KT)^(-1/3)))*(1+(3.82*y8./KT)+1.51*((y8./KT)^2)+0.144*(y8./KT)^3-1.14*(10^-2)*(y8./KT)^4)./(6.023*10^23);
Q4 =(2.58*10^3)*((y8./KT)^(-2/3))*exp(-3.721*((y8./KT)^(-1/3)))*(1+(3.96*y8./KT)+0.116*(y8./KT)^2)./(6.023*10^23);
Q5 = ((5.59*10^10)*(((y8./KT))^(-2/3))*exp(-12.277*((y8./KT)^(-1/3)))*(1-0.135*(y8./KT)+2.54*0.01*((y8./KT)^2)-1.29*0.001*((y8./KT)^3)))./(6.023*10^23);
D = (2.07*10^14)*((y8./KT)^(3/2))*(1-0.860*((y8./KT)^(1/2))+0.429*(y8./KT))*exp(-25.82/(y8./KT));
nB = (0.6*10^-9)*(((2*1.202)./(pi.^2))*(((10^6)*sy0.*8065.73).^3));
nP = 0.75*nB;
nN = 0.25*nB;
nEn = ((((3*1.202)./(2*pi.^2))*(((10^6)*sy0.*8065.73).^3)))+ nP;
nEp = ((((3*1.202)./(2*pi.^2))*(((10^6)*sy0.*8065.73).^3)))*(exp((-0.511)./(sy0)));
Wtn2 = 1000;
Wconst2 = ((1.239*10^-10)^3); % MeV^3
Wb2 = ((7.56*10^-16)*((1.239*10^-6)^3))./((1.6*10^-19)*((8.617*10^-5)^4));
WV2 = (3*10^10)*sqrt(1-(1./((y8/0.511)+1))^2);
WF2 = (((1.166*10^-11)./(8065.73*10^6))^2)*((y8)^2)*(exp(-(0.783)./y8)); 
WF1 = (((1.166*10^-11)./(8065.73*10^6))^2)*((y8)^2);
L1 = (y3./Wtn2)+(y5*D)-(y1*y4*WF2*WV2)-(y1*y2*WF1*WV2);
L2 = (((y4)^2)*Q2*0.5)-(y2*y3*WF1*WV2)-(y1*y2*WF1*WV2);
L3 = (y1*y4*WF2*WV2)+(y5*D)-(y2*y3*WF1*WV2)-(y3./Wtn2);
L4 = (y3./Wtn2)+(y2*y3*WF1*WV2)+(y5*D)+(((y6)^2)*Q5)-(y1*y4*WF2*WV2)-(((y4)^2)*Q2*0.5)-(y4*y5*Q4);
L5 = (((y4)^2)*Q2*0.5)-(y5*D)-(y4*y5*Q4);
L6 = (y4*y5*Q4)-(((y6)^2)*Q5*0.5);
L7 = (((y6)^2)*Q5*0.5);
S1 = (((((y4)^2)*Q2*0.5)*1.44)-((y5*D)*2.22)+((y4*y5*Q4)*5.49)+((((y6)^2)*Q5*0.5)*12.86));
S2 = (((y2*y3*WF1*WV2))+((y1*y4*WF2*WV2))+(2*(y1*y2*WF1*WV2))+((y3./Wtn2))+((((y4)^2)*Q2*0.5)))*y8;
L8 = ((Wconst2).*(S1-S2))./(4*Wb2.*((y8)^3));
ode1 = diff(y1)==L1;
ode2 = diff(y2)==L2;
ode3 = diff(y3)==L3;
ode4 = diff(y4)==L4;
ode5 = diff(y5)==L5;
ode6 = diff(y6)==L6;
ode7 = diff(y7)==L7;
ode8 = diff(y8)==L8;
cond1 = y1(0)==nEn;
cond2 = y2(0)==nEp;
cond3 = y3(0)==nN;
cond4 = y4(0)==nP;
cond5 = y5(0)==0;
cond6 = y6(0)==0;
cond7 = y7(0)==0;
cond8 = y8(0)==0.1;
odes = [ode1;ode2;ode3;ode4;ode5;ode6;ode7;ode8];
conds = [cond1;cond2;cond3;cond4;cond5;cond6;cond7;cond8];
[y1Sol,y2Sol,y3Sol,y4Sol,y5Sol,y6Sol,y7Sol,y8Sol] = dsolve([odes,conds]);
t = linspace(10^2,10^5,length(y7Sol));
loglog(t,y7Sol ,'k-','linewidth',2)

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Answer 1

John D'Errico 2021-11-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1579324-explicit-solution-could-not-be-found#answer_823972

编辑：John D'Errico 2021-11-4

And, your question is? What does this mean:

"Explicit solution could not be found"

Surely, if it just tried harder, it would find a solution. Except that most such problems will have no analytical solution. This is why numerical solvers exist.

So learn to use tools like ODE45, etc. There is no assurance it will not have problems, but there are other such numerical solvers in that family too.

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Answer 2

Walter Roberson 2021-11-4

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https://ww2.mathworks.cn/matlabcentral/answers/1579324-explicit-solution-could-not-be-found#answer_823989

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C = 3*10^10;
KT = 0.086173324;  % MeV

You have some constants that are only given to one significant digit. You have other constants that are given to 8 significant digits.

You are using dsolve(), which asks for an exact indefinitely precise solution. But does it make sense to ask for an exact solution when your significant digits vary so widely ?

You also have not been careful about how your decimal-written values are converted to symbolic numbers, so the number of significant figures is not being preserved. MATLAB is trying to find approximations to the numbers. I just counted, and at one point in your expression, MATLAB is trying to work with a constant that is 116 digits long. How can it possibly make sense to ask for an exact solution to in this kind of situation?

How, for example, can you justify using 8 significant digits for KT but not using higher resolution for the speed of light, which should be 299792458 m/s ? And are you sure you should be using 3E10 instead of 3E8 ? Are you calculating in centimeters ??