If you have ever worked with numerical methods you will know that a major issue with using these methods is not only the exactness of the method but most time, we struggle too with stability of each of the methods.

In this post I am simply going to give a Matlab code which you can copy and paste into your Matlab, simulate and get a plot representing the stable and the unstable region of these two numerical methods:

- Euler Method
- Runge Kutta method

Learn more about the A stability.

## Matlab code

clear all x=-4:0.01:4; y=-4:0.01:4; [email protected](x,y) sqrt((1+x)^2+(y)^2); [email protected](x,y) sqrt((1+x+0.5*(x^2-y^2))^2+(y+x*y)^2); subplot(1,2,1) title('Euler Method') subplot(1,2,2) title('RK-method') for i=1:2 if i==1 fun=f1; else if i==2 fun=f2; end end for m=1:length(x) for n=1:length(y) if fun(x(m),y(n))<1 z(n,m)=1; else z(n,m)=0; end end end subplot(1,2,i) imagesc(x,y,z);%stability region if i==1 title('Euler Method'); else if i==2 title('RK'); xlabel('Re(lambda*h)'); ylabel('Im(lambda*h)'); end end end

## Figures

### Euler method

### Runge Kutta method

The Blue area represents the unstable region and the red area represents the stable region.

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