computation of symbolic terms and error analysis

tic
syms x y m %alpha beta b lambda eta phi
phi=sqrt(0.5)
b=10
eta=1
alpha=2;
beta=1;
T=zeros(1,2,’sym’);
G=zeros(1,2,’sym’);
A=zeros(1,’sym’);
B=zeros(1,’sym’);
C=zeros(1,’sym’);
D=zeros(1,’sym’);
E=zeros(1,’sym’);
F=zeros(1,’sym’);
G_val=zeros(1,’sym’);
series(x)=sym(zeros(1,1));
series1(x)=sym(zeros(1,1));
% Transform Initial condition
T(1)=m;
T(2)=0;
% Initial transform value of exp function

for i=1:4
G(i)=y;
if i==1
E(1)=exp((eta*T(1))/(eta+T(1)));
else
A(1)=0;
for j=1:i-1
E(i)=A(1)+(j/(i-1))*G(j)*E(i-j);
end
B(1)=0;
for j=1:i
B(1)=B(1)+T(j)*G(i-j+1);
end
eq1=G(i)-T(i)+(1/eta)*B(1);
G_val=simplify(solve(eq1,y));
G(i)=simplify(G_val);
E_val=subs(E(i),y,G_val);
E(i)=E_val
end
C(1)=0
for r=1:i
C(1)=C(1)+T(r)*E(i-r+1);
end
T(i + alpha*beta) = (phi^2*C(1)-b*phi^2*E(i))*(gamma(1+(sym(i-1)/beta))/gamma(1+alpha+(sym(i-1)/beta)));
%T(i+2)=simplify((1/(i*(i+1)))*(phi^2*C(1)-b*phi^2*E(i)));
end

for k=1:3
series(x)=simplify(series(x)+T(k)*(power(x,((k-1)*beta))));
end
series
e1=subs(series,x,1);
format long
accuracy=input(‘enter the accuracy’)
f=e1(x)
g=inline(f)
a=input(‘enter the ist approximation=’)
b=input(‘enter the 2nd approximation=’)
fa=feval(g,a)
fb=feval(g,b)
while fa*fb>0
a=input(‘enter the ist approximation=’)
b=input(‘enter the 2nd approximation=’)
fa=feval(g,a)
fb=feval(g,b)
end
for i=1:50
c=(a+b)/2;
fc=feval(g,c);
disp([i a fa b fb c fc abs(b-a)])
if fc==accuracy
fprintf(‘the root of the equation is %f’,c)
break;
elseif abs(b-a)<=accuracy
fprintf(‘the root of the equation is %f’,c)
break;
elseif fa*fc<=0
b=c;
fb=fc;
else
a=c;
fa=fc;
end
end
fprintf(‘the value of c=%f’, c);
series1(x)=subs(series,m,c)
residualError=sym(zeros(1,1));
residual=sym(zeros(1,1));
residualError(x) = abs(diff(series1,x,2)+ B*phi^2*(1-(series1)/B)*exp((eta*series1)/(eta+series1)))
residual_error=double(subs(residualError,x,0.2))
var =double(residual_error);
x=0:0.1:1
error=zeros(1)
row=0;
for i=1:length(x)
row=row+1;
error(row)=(residualErrorx(i))
max_error=max(error)
end
fprintf(‘The residual error is %fn’, max_error);
%—————————————————————–
the error appear as Error using mupadengine/evalin2double
Unable to convert expression containing symbolic variables into double array. Apply ‘subs’ function first to substitute values for variables.

Error in mupadengine/feval2double

Error in sym/double (line 756)
X = feval2double(symengine, "symobj::doubleDirect", S);
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Related documentation
now i substutite the value of m using sysntax series1(x)=subs(series,m,c) but when i later on call series 1 in line residualError(x) = abs(diff(series1,x,2)+ B*phi^2*(1-(series1)/B)*exp((eta*series1)/(eta+series1))) the final expression is having m and y . That is symbolic and craet an errortic
syms x y m %alpha beta b lambda eta phi
phi=sqrt(0.5)
b=10
eta=1
alpha=2;
beta=1;
T=zeros(1,2,’sym’);
G=zeros(1,2,’sym’);
A=zeros(1,’sym’);
B=zeros(1,’sym’);
C=zeros(1,’sym’);
D=zeros(1,’sym’);
E=zeros(1,’sym’);
F=zeros(1,’sym’);
G_val=zeros(1,’sym’);
series(x)=sym(zeros(1,1));
series1(x)=sym(zeros(1,1));
% Transform Initial condition
T(1)=m;
T(2)=0;
% Initial transform value of exp function

Error in mupadengine/feval2double

Error in sym/double (line 756)
X = feval2double(symengine, "symobj::doubleDirect", S);
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Related documentation
now i substutite the value of m using sysntax series1(x)=subs(series,m,c) but when i later on call series 1 in line residualError(x) = abs(diff(series1,x,2)+ B*phi^2*(1-(series1)/B)*exp((eta*series1)/(eta+series1))) the final expression is having m and y . That is symbolic and craet an error tic
syms x y m %alpha beta b lambda eta phi
phi=sqrt(0.5)
b=10
eta=1
alpha=2;
beta=1;
T=zeros(1,2,’sym’);
G=zeros(1,2,’sym’);
A=zeros(1,’sym’);
B=zeros(1,’sym’);
C=zeros(1,’sym’);
D=zeros(1,’sym’);
E=zeros(1,’sym’);
F=zeros(1,’sym’);
G_val=zeros(1,’sym’);
series(x)=sym(zeros(1,1));
series1(x)=sym(zeros(1,1));
% Transform Initial condition
T(1)=m;
T(2)=0;
% Initial transform value of exp function

Error in mupadengine/feval2double

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