*[I split this off as a separate Question, cleaned up the machine-generated Title, added the Tags, and cleaned out some excessive blank lines.---Carl Love as Moderator]*

could anyone help me with my euler plot too!

**> ****with(plots):with(DEtools):**

Equations & Initial conditions

**> ****de1:=D(x)(t)=a*x(t)-q*x(t)*y(t)-n*x(t)*z(t);**

**> ****de2:=D(y)(t)=-b*y(t)+k*x(t)*y(t);**

**> ****de3:=D(z)(t)=-c*z(t)+m*x(t)*z(t);**

**> **

**> ****a:=4.43:q:=0.022:b:=0.89:k:=0.00062:c:=0.25:m:=0.25:n:=1:T:=4:h:=0.2:N:=T/h:**

**> ****soln:=dsolve({de1,de2,de3,x(0)=10,y(0)=10,z(0)=10},{x(t),y(t),z(t)},numeric):**

**> ****odeplot(soln,[[t,x(t),color=green],[t,y(t),color=blue],[t,z(t),color=red]],0..100,numpoints=100,title=Rabbit_v_fox_stoat):pexact:=%:**

**> ****DEplot3d([de1,de2,de3],[x(t),y(t),z(t)],t=0..100,[[x(0)=10,y(0)=10,z(0)=10]],x=0..20,y=0..20,z=0..20,linecolor=black,arrows=medium,animatecurves=true,numframes=100):xyzexact:=%:**

My numerical solve (Euler's method & 4th order)

**> ****ESys:=proc(t,x,y,z,q,N)**

**> ****local f,g,e,n,k1,l1,m1;**

**> ****f:=(x,y,z)->a*x-q*x*y-n*x*z;**

**> ****g:=(x,y,z)->-b*y+k*x*y;**

**> ****e:=(x,y,z)->-c*z+m*x*z;**

**> ****for n from 0 to N do**

**> ****k1:=h*f(x[n],y[n],z[n]);**

**> ****l1:=h*g(x[n],y[n],z[n]);**

**> ****m1:=h*e(x[n],y[n],z[n]);**

**> ****t[n+1]:=t[n]+h;**

**> ****x[n+1]:=x[n]+k1;**

**> ****y[n+1]:=y[n]+l1;**

**> ****z[n+1]:=z[n]+m1;**

**> ****od;**

**> ****end proc:**

**> **

**> ****Fourth:=proc(t,x,y,z,q,N)**

**> ****local f,g,e,n,k1,k2,k3,k4,l2,l1,l3,l4,m1,m2,m3,m4;**

**> ****f:=(x,y,z)->a*x-q*x*y-n*x*z;**

**> ****g:=(x,y,z)->-b*y+k*x*y;**

**> ****e:=(x,y,z)->-c*z+m*x*z;**

**> ****for n from 0 to N do**

**> ****k1:=h*f(x[n],y[n],z[n]);**

**> ****l1:=h*g(x[n],y[n],z[n]);**

**> ****m1:=h*e(x[n],y[n],z[n]);**

**> ****k2:=h*f(x[n]+0.5*h,y[n]+0.5*k1,z[n]+0.5*k1);**

**> ****l2:=h*g(x[n]+0.5*h,y[n]+0.5*l1,z[n]+0.5*l1);**

**> ****m2:=h*e(x[n]+0.5*h,y[n]+0.5*m1,z[n]+0.5*m1);**

**> ****k3:=h*f(x[n]+0.5*h,y[n]+0.5*k2,z[n]+0.5*k2);**

**> ****l3:=h*g(x[n]+0.5*h,y[n]+0.5*l2,z[n]+0.5*l2);**

**> ****m3:=h*e(x[n]+0.5*h,y[n]+0.5*m2,z[n]+0.5*m2);**

**> ****k4:=h*f(x[n]+h,y[n]+k3,z[n]+k3);**

**> ****l4:=h*g(x[n]+h,y[n]+l3.z[n]+l3);**

**> ****m4:=h*e(x[n]+h,y[n]+m3,z[n]+m3);**

**> ****t[n+1]:=t[n]+h;**

**> ****x[n+1]:=x[n]+((1)/(6))*(k1+2*k2+2*k3+k4);**

**> ****y[n+1]:=y[n]+((1)/(6))*(l1+2*l2+2*l3+l4);**

**> ****z[n+1]:=y[n]+((1)/(6))*(m1+2*m2+2*m3+m4);**

**> ****od;**

**> ****end proc:**

Initial conditions

**> ****t[0]:=0:x[0]:=10:y[0]:=10:z[0]:=10:**

Step length and number of steps

**> ****h:=0.2:N:=T/h:**

Get the numerical solution

**> ****ESys(t,x,y,z,q,N):**

**> ****seq([t[n],evalf(x[n]),evalf(y[n]),evalf(z[n])],n=0..N):**

Plot against the Maple's numerical solution

**> ****ax:=plot({seq([t[n],x[n]],n=0..N)},style=point,colour=black):**

**> ****ay:=plot({seq([t[n],y[n]],n=0..N)},style=point,colour=black):**

**> ****az:=plot({seq([t[n],z[n]],n=0..N)},style=point,colour=black):**

**> ****axyz:=plot({seq([x[n],y[n],z[n]],n=0..N)},style=point,colour=black):**

**> **

**> ****display(array([display(pexact,ax,ay,az),display(xyzexact,axyz)]));**

Error, (in plot) found points with fewer or more than 2 components

Error, (in plots:-display) expecting plot structure but received: axyz

Initial conditions

**> ****t[0]:=0:x[0]:=10:y[0]:=10:z[0]:=10:**

Step length and number of steps

**> ****h:=0.2:N:=T/h:**

Get the numerical solution

**> ****Fourth(t,x,y,z,q,N):**

**> ****seq([t[n],evalf(x[n]),evalf(y[n]),evalf(z[n])],n=0..N):**

Plot against the Maple's numerical solution

**> ****ix:=plot({seq([t[n],x[n]],n=0..N)},style=point,colour=black):**

**> ****iy:=plot({seq([t[n],y[n]],n=0..N)},style=point,colour=black):**

**> ****iz:=plot({seq([t[n],z[n]],n=0..N)},style=point,colour=black):**

**> ****ixyz:=plot({seq([x[n],y[n],z[n]],n=0..N)},style=point,colour=black):**

**> **

**> ****display(array([display(pexact,ix,iy,iz),display(xyzexact,ixyz)]));**

Error, (in plot) found points with fewer or more than 2 components

Error, (in plots:-display) expecting plot structure but received: ixyz