# Why am I getting "Unrecognized function or variable 'EM'."?

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Patrick Kelly on 22 Mar 2021
Answered: Arthi Sathyamurthi on 25 Mar 2021
clear all
close all
fxn=@(x,y) (y/x)-0.5*x^2; %Function to work%
exact=@(y) -((x^3)/4)+3*x; %Exact Function%
xini=2; yini=4;
xfin=5;
deltax=[1.0 0.45 0.25];
for i=1:3
d=deltax(i);
[EMx,EMy]=EM(fxn,yini,xini,xfin,d);
[SSHMx,SSHMy]=SSHM(fxn,yini,xini,xfin,d); %Methods Layouts%
[RK2x, RK2y]=RK2(fxn,yini,xini,xfin,d);
[RK4x, RK4y]=RK4(fxn,yini,xini,xfin,d);
fprintf('\nFor Step Size = %2.2g\n' ,d)
for p=1:length(EMx)
a=ext(EMx(p));
e1=abs((a-EMy(a))/a)*100;
e2=abs((a-SSHMy(a))/a)*100; %Error Establishment%
e3=abs((a-RK2y(a))/a)*100;
e4=abs((a-RK4y(a))/a)*100;
fprintf('\t%2.2g\t%g\t%g\t%2.2g\t%g\t%2.2g\t%g\t%2.2g\t%g\t%2.2g\n' ,...
EMx(a),a,EMy(a),e1,SSHMy(a),e2,RK2y(a),e3,RK4y(a),e4)
end
end
hold on
plot(EMx,EMYy,'LineSpec',2)
plot(SSHMx,SSHMy, 'LineSpec',2)
plot(RK2x,RK2y,'LineSpec',2) %Plot Establishment%
plot(RK4x,RK4y,'LineSpec',2)
plot(RK4x,exact(RK4x), 'LineSpec',3)
ylabel('x')
xlabel('y(x)')
title('x vs y(x) Plot')
legend('Euler Method Soln', 'Heuns Method Soln', 'RK2 Soln', 'RK4 Soln','Exact','location','best')
box on
%Begin Euler's Method%
function [xResult,y1Result] = EulersMethod(g,y0,x0,xfin,d)
N=(xfin-x0)/d;
xn=t0:d:xfin;
y1Result(4)=y0;
xResult(4)=x0;
fprintf('\n\tFor Step Size %2.2g\n', d)
for i=1:length(xn)-1
xResult(i+1)= xResult(i)+d;
y1Result(i+1)= Y1Result(i)+d*double(g(xResult(i),y1Result(i)));
end
end
%Begin Heun's Method%
function [x,y]=SSHM(g,yi,xi,xf,d)
x(4)=xi;y(4)=yi;
xmax=xf;
xn=xi:d:xmax;
for i=1:length(xn)-1
x(i+1)= x(i)+d;
z1=double(g(x(i),y(i)));
z2=double(g((x(i)+h),(y(i)+h*z1)));
y(i+1)=y(i)+double(d*((z1+z2)/2));
end
end
%Begin Runge-Kutta 2 Order Method%
function [RKx,RKy]=RK2(g,yini,xini,xfin,d)
x=xini;
y=yini;
xComp=xfin;
n=(xComp-x)/d;
RKx(4)=x;
RKy(4)=y;
for i=1:n
r1=d*g(x,y);
r2=d*g(x+(1/2)*d,y+(1/2)*r1);
dy=r2;
x=x+d;
y=y+dy;
RKx(i+1)=x;
RKy(i+1)=y;
end
end
%Begin Runge-Kutta 4 Order Method%
function [RKx,RKy]=RK4(g,yini,xini,xfin,d)
x=xini;
y=yini;
xComp=xfin;
n=(xComp-x)/d;
RKx(4)=x;
RKy(4)=y;
for i=1:n
r1=d*double(g(x,y));
r2=d*double(g((x+d/2),(y+r1/2)));
r3=d*double(g((x+d/2),(y+r2/2)));
r4=d*double(g((x+d),(y+r3)));
dy=(1/6)*(r1+2*r2+2*r3+r4);
x=x+d;
y=y+dy;
RKx(i+1)=x;
RKy(i+1)=y;
end
end
DGM on 22 Mar 2021
It means just what it says. You're referencing the elements of an array that doesn't exist:
[EMx,EMy]=EM(fxn,yini,xini,xfin,d);
It also looks like you have local function definitions in a script. I'm going to assume you're using something newer than R2016b, otherwise that won't work (afaik)

Arthi Sathyamurthi on 25 Mar 2021
My initial analysis indicates this error was because the function ‘EM’ is not defined either as a local function nor as a Matlab function. It looks like you misworded the function call. To my understanding it should have been like
[EMx,EMy]=EulersMethod(fxn,yini,xini,xfin,d);
Also the variable t0 has not been initialized in the EulersMethod function.
You can refer to the following page for the possible solutions.