Numerical solving second order differential equation
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I would like to solve a second order differential equation,please see the attachment. I used the following code:
b = 0.19;
a = 0.072;
beta = 0.72;
Pr = 0.72;
c = beta/Pr*a^(4/3);
xspan = [0.01 100];
g40 = [1 0];
opts = odeset('RelTol',1e-4,'AbsTol',1e-6);
[x4,g4] = ode45(@(x4,g4) model4ode(x4,g4,b,c), xspan, g40, opts);
plot(log10(x4),g4)
function dg4dx4 = model4ode(x4,g4,b,c)
dg4dx4 = zeros(2,1);
dg4dx4(1) = g4(2);
dg4dx4(2) = (2./(3*x4)).*(4+x4.^(2*b).*(x4.^(2*b)+1).^(-1)).*g4(2)+...
((22/3)*c*x4.^(-2/3).*(x4.^(2*b)+1).^(1/(3*b))-(22/9)*x4.^(2*b-2).*(x4.^(2*b)+1).^(-1)).*g4(1);
end
But the result is not true. Could someone help me?
回答（1 个）
Torsten
2018-1-8
b = 0.19;
a = 0.072;
beta = 0.72;
Pr = 0.72;
c = beta/Pr*a^(4/3);
xspan = [0.01 100];
g40 = [(xspan(1)^(2*b)+1)^(-1/(3*b))*(-11/3) 22/3*c*xspan(1)^(1/3)];
opts = odeset('RelTol',1e-4,'AbsTol',1e-6);
[x4,g4] = ode45(@(x4,g4) model4ode(x4,g4,b,c), xspan, g40, opts);
f4(:,1)=3/22*1/c*x4(:).^(-1/3).*g4(:,2);
f4(:,2)=(g4(:,1).*(x4(:).^(2*b)+1).^(1/(3*b))+0.5*1/c*x4(:).^(-1/3).*g4(:,2))./x4(:);
plot(log10(x4),f4)
function dg4dx4 = model4ode(x4,g4,b,c)
dg4dx4 = zeros(2,1);
dg4dx4(1) = g4(2);
dg4dx4(2) = (22/3*c*x4^(1/3)*(x4^(2*b)+1)^(1/(3*b))*g4(1)+g4(2)*(11+x4)/3)/x;
end
Best wishes
Torsten.
4 个评论
Star Strider
2018-1-9
What differential equation solver does ‘the literature’ use?
I would trust the MATLAB solver results.
Torsten
2018-1-9
Could you include "the literature" as a pdf or a link ?
Best wishes
Torsten.
Xiang Yi
2018-1-9
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