solution of coupled differential equation
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i am trying to solve some couples differential equation , the equations are given in the attachment .
can these equations be solved using [ode45 command ]
if i get some reference for similar type of equation that will be quiet helpful
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Torsten
2022년 8월 28일
편집: Torsten
2022년 8월 28일
syms z11(x) z12(x) z21(x) z22(x) z31(x) z32(x)
eqn1 = diff(z11) == z12;
eqn2 = diff(z12) + z12 + z22 + z31 - 5 == 0;
eqn3 = diff(z21) == z22;
eqn4 = diff(z22) + z12 + z22 + z32 - 4 == 0;
eqn5 = diff(z31) == z32;
eqn6 = diff(z32) - z22 + z11 + z31 - 3 == 0;
eqns = [eqn1,eqn2,eqn3,eqn4,eqn5,eqn6];
conds = [z11(0)==0,z21(0)==0,z31(0)==0,z11(1)==0,z21(1)==0,z31(1)==0];
sol = dsolve(eqns,conds)
bvpfcn = @(x,y)[y(2);-y(2)-y(4)-y(5)+5;y(4);-y(2)-y(4)-y(6)+4;y(6);y(4)-y(1)-y(5)+3];
bcfcn = @(ya,yb) [ya(1);ya(3);ya(5);yb(1);yb(3);yb(5)];
xmesh = linspace(0,1,100);
solinit = bvpinit(xmesh, [0 0 0 0 0 0]);
sol = bvp4c(bvpfcn, bcfcn, solinit);
plot(sol.x, [sol.y(1,:);sol.y(3,:);sol.y(5,:)])
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Sam Chak
2022년 8월 27일
Hi @asim asrar
The second-order coupled system looks like a boundary value problem, where you need to find the initial values of
,
,
to satisfy the boundary values requirements.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1109665/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1109670/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1109675/image.png)
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Torsten
2022년 8월 28일
but i think bvp4c is meant for single differential equation, but mine is coupled differential equation
If you had looked at the examples provided, you would have seen that this is not true.
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