solving multiple equation in a for loop

hi

i have these equations and i dont know how to solve them plz help me ASAP

thanks

clc
clear all
%%part b
dt=1 ;V=1000*1000*100 ; pro=0.15 ; Co=10^-6 ; alpha =5.615; Bo=1.35;
beta =1.127 ;Ax=1000*100 ; mio=1 ;Dx=1000;Kx=20*10^-3;

cte=(V*pro*Co)/(alpha*Bo*dt);
T=(beta * Ax* Kx)/(mio *Bo*Dx);
p1(1:360)=5000 ; p2(1)=5000; p3(1)=5000;p4(1)=5000 ; p5(1)=5000; p6(1)=5000;
p7(1)=5000 ; p8(1)=5000; p9(1)=5000;
for i=1:1:360
    p3(i+1)*T-(cte +2*T)*p2(i+1)+T*p1(i+1)==-(cte *p2(i));
    p4(i+1)*T-(cte +2*T)*p3(i+1)+T*p2(i+1)==-(cte *p2(i)-250);
    p5(i+1)*T-(cte +2*T)*p4(i+1)+T*p3(i+1)==-(cte *p3(i));
    p6(i+1)*T-(cte +2*T)*p5(i+1)+T*p4(i+1)==-(cte *p4(i));
    p7(i+1)*T-(cte +2*T)*p6(i+1)+T*p5(i+1)==-(cte *p5(i));
    p8(i+1)*T-(cte +2*T)*p7(i+1)+T*p6(i+1)==-(cte *p6(i)-250);
    p9(i+1)*T-(cte +2*T)*p8(i+1)+T*p7(i+1)==-(cte *p7(i));
    -(cte +2*T)*p9(i+1)+T*p8(i+1)==-(cte *p8(i));
end

Answer 1

[Walter Roberson]

%%part b
dt=1 ;V=1000*1000*100 ; pro=0.15 ; Co=10^-6 ; alpha =5.615; Bo=1.35;
beta =1.127 ;Ax=1000*100 ; mio=1 ;Dx=1000;Kx=20*10^-3;

cte=(V*pro*Co)/(alpha*Bo*dt);
T=(beta * Ax* Kx)/(mio *Bo*Dx);
p1(1:360)=5000 ; p2(1)=5000; p3(1)=5000;p4(1)=5000 ; p5(1)=5000; p6(1)=5000;
p7(1)=5000 ; p8(1)=5000; p9(1)=5000;
syms p2i1 p3i1 p4i1 p5i1 p6i1 p7i1 p8i1 p9i1
for i=1:1:359
    eqn = [
            p3i1*T-(cte +2*T)*p2i1+T*p1(i+1)==-(cte *p2(i));
            p4i1*T-(cte +2*T)*p3i1+T*p2i1==-(cte *p2(i)-250);
            p5i1*T-(cte +2*T)*p4i1+T*p3i1==-(cte *p3(i));
            p6i1*T-(cte +2*T)*p5i1+T*p4i1==-(cte *p4(i));
            p7i1*T-(cte +2*T)*p6i1+T*p5i1==-(cte *p5(i));
            p8i1*T-(cte +2*T)*p7i1+T*p6i1==-(cte *p6(i)-250);
            p9i1*T-(cte +2*T)*p8i1+T*p7i1==-(cte *p7(i));
            -(cte +2*T)*p9i1+T*p8i1==-(cte *p8(i))
    ];
    S = solve(eqn, [p2i1, p3i1, p4i1, p5i1, p6i1, p7i1, p8i1, p9i1]);
    p2(i+1) = S.p2i1;
    p3(i+1) = S.p3i1;
    p4(i+1) = S.p4i1;
    p5(i+1) = S.p5i1;
    p6(i+1) = S.p6i1;
    p7(i+1) = S.p7i1;
    p8(i+1) = S.p8i1;
    p9(i+1) = S.p9i1;
end

p2(1:10)

ans = 1×10

5.0000 4.9800 4.9638 4.9516 4.9426 4.9359 4.9310 4.9274 4.9248 4.9229

p3(1:10)

ans = 1×10

5.0000 4.9362 4.9085 4.8888 4.8745 4.8640 4.8563 4.8506 4.8465 4.8435

p4(1:10)

ans = 1×10

5.0000 4.9667 4.9181 4.8869 4.8647 4.8486 4.8368 4.8283 4.8220 4.8175

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p5(1:10)

ans = 1×10

5.0000 4.9576 4.9062 4.8594 4.8262 4.8024 4.7852 4.7727 4.7637 4.7571

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p6(1:10)

ans = 1×10

5.0000 4.8984 4.8227 4.7623 4.7158 4.6825 4.6585 4.6413 4.6288 4.6197

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p7(1:10)

ans = 1×10

5.0000 4.7187 4.5792 4.4946 4.4352 4.3922 4.3613 4.3392 4.3232 4.3116

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p8(1:10)

ans = 1×10

5.0000 4.3553 4.1070 3.9878 3.9168 3.8681 3.8333 3.8083 3.7903 3.7774

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p9(1:10)

ans = 1×10

5.0000 3.2278 2.9100 2.7802 2.7135 2.6718 2.6428 2.6220 2.6070 2.5963

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