Need help with three interdependent differential equation. Not able to obtain accurate graph.

Simultaneous first-order ordinary differential equations: dv/dx= 2P/r - [C(x) - Co] where v = 0 at x = 0; dC/dx=B where C = Co=0.30 at x = L; and dB/dx=(C(dv/dx)+vB-2N/r)/D

Where N=10^-5 when x≤10 And N=0 when x>10

I'm trying to graph C and V with respect to by using a forward finite method.

nsteps= 1000;

Co= 0.3;

N=(1*(10^-5)) ;

D= (1*(10^-5));

R= 0.05;

P= (2*(10^-5));

W= (2*P)/R;

z1= 0;

z2= 0.75;

z3= 0;

dx= 0.1;

xplot= zeros(1, nsteps);

z1plot= zeros(1, nsteps);

z2plot= zeros(1, nsteps);

z3plot= zeros(1, nsteps);

for j= 1:nsteps

    x= j*dx;

    if x<=10

        N==N;

    else
        N==0;
        if x<=100
            z2==0.3;
        else
            z2==z2;

    z1= ((W*(z2-Co)*dx)+z1);
    z2= ((z3*dx)+z2);
    z3= ((((W/D)*z2*(z2-Co))+ ((z1*z3)/D)- ((2*N)/(R*D)))*dx)+z3;

    xplot(j)=x;
    z1plot(j)=z1;
    z2plot(j)=z2;
    z3plot(j)= z3; 
        end 
        end

end

plot(xplot, z2,'x')

I don't know whats wrong.

[RahulTandon]

i'm taking it that you are tring to plot with respect to x

[RahulTandon]

Too many equations is the error message that ia am geting!!

Answer 1

[RahulTandon]

%% Simultaneous first-order ordinary differential equations: clc; syms x v(x) C(x) C0 B L N(x) r E clear; %% cannot use D as a variable!! str1 = 'Dv == 2*P/r - [C(x) - Co]'; str2 = 'v(0) = 0'; str3 = 'DC == B '; str4 ='C(L) = Co'; str5 = 'C0 = 0.30'; str6 = 'dB/dx == (C*Dv+v*B-2*N/r)/E';

str7 = 'N(9) = 10^-5'; % when x<=10 str8 = 'N(11) = 0'; % when x>10

[C,v] = dsolve(str1,str2,str3,str4,str5,str6,str7,str8,'x')