MATLAB: Simple symbolic system of nonlinear equations

equationsnonlinearSymbolic Math Toolboxsystem

I have a simple system of linear equations such as

f(x,y,z)=a

g(x,y,z)=b

h(x,y,z)=c

with f,g,h being specified polynomial functions. I want to find the symbolic solution x=x(a,b,c), y=y(a,b,c) and z=z(a,b,c).

Any help on coding this problem is much appreciated

Best Answer

 sol = solve([f==a, g==b, h==c], [x, y, z])

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MATLAB: Solving multiple symbolic equations to get (X/Z)

Hi,

i guess you want this:

syms X Y Z a b c d
eqn(1) = X == a * Y + b * Z;
eqn(2) = Y == c * X + d * Z;
sol = solve(eqn,[X Z]);
x = sol.X
z = sol.Z

which is:

x =
(Y*b + Y*a*d)/(d + b*c)
z =
(Y - Y*a*c)/(d + b*c)

Best regards

Stephan

MATLAB: How can i call array elements in a plot3 function

s=10;b=8/3; r=28;h=0.003; a=28
x=0;y=1; z=0; f=zeros(1,3); f=[x y z]; 
k=1;
for t=0:h:100 
    k1_x=a*(y(k)-x(k));
    k2_x=a*(y(k)-x(k))+(k1_x*h*0.5);
    k3_x=a*(y(k)-x(k))+(k2_x*h*0.5);
    k4_x=a*(y(k)-x(k))+(k3_x*h);
    x(k+1)=x(k)+(k1_x+2*k2_x+2*k3_x+k4_x)*h/6; 
    k1_y=x(k)*(r-z(k))-y(k);
    k2_y=(x(k)*(r-z(k))-y(k))+k1_y*h*0.5;
    k3_y=(x(k)*(r-z(k))-y(k))+k2_y*h*0.5;
    k4_y=(x(k)*(r-z(k))-y(k))+k3_y*h*0.5;
    y(k+1)=y(k)+(k1_y+(2*k2_y)+(2*k3_y)+(k4_y))*h/6; 
    k1_z=x(k)*y(k)-b*z(k);
    k2_z=(x(k)*y(k)-b*z(k))+k1_z*h*0.5;
    k3_z=(x(k)*y(k)-b*z(k))+k2_z*h*0.5;
    k4_z=(x(k)*y(k)-b*z(k))+k3_z*h*0.5;
    z(k+1)=z(k)+(k1_z+(2*k2_z)+(2*k3_z)+(k4_z))*h/6; 
    k=k+1;
end
    plot3(x,y,z); grid on; xlabel('x'); ylabel('y');
    zlabel('z'); title('Lorenz attractor');

Best Answer

Related Solutions

MATLAB: Solving multiple symbolic equations to get (X/Z)

MATLAB: How can i call array elements in a plot3 function

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