solution of coupled differential equation

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

Answer 1

[Torsten]

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,:)])

[asim asrar]

dear torsten,

it seems as if the code goes into an infinite loop after execution.

[Torsten]

These are alternative codes to solve your equations. Either use the first or the last.

I could not test the first code because the execution time was too long.

The second code produces results (see above).

Answer 2

[Sam Chak]

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.

Try referring to the examples in the bvp4c documentation.

[asim asrar]

but i think bvp4c is meant for single differential equation, but mine is coupled differential equation

[Torsten]

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.