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how i can subs. true??

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sadeem alqarni
sadeem alqarni on 11 Apr 2018
Closed: MATLAB Answer Bot on 20 Aug 2021
syms xn h r s y(xn) ya ya2
q1=xn+2*h;
q2=xn+h;
q3=xn+r*h;
q4=xn+s*h;
f1=y(q1);
f2=y(q2);
f3=diff(y(q3),3);
f4=diff(y(q4),3);
f5=diff(y(q1),3);
f6=diff(y(q1));
f7=diff(y(q2),3);
f8=diff(y(q1),2);
f9=y(q3);
f10=diff(y(q2));
f11=diff(y(q2),2);
f12=diff(y(q3));
f13=diff(y(q3),2);
f14=y(q4);
f15=diff(y(q4));
f16=diff(y(q4),2);
k=sum(taylor(f8,h,'order',10));
z=sum(taylor(f1,h,'order',10));
w=sum(taylor(f2,h,'order',10));
m=sum(taylor(f3,h,'order',10));
x=sum(taylor(f4,h,'order',10));
p=sum(taylor(f5,h,'order',10));
b=sum(taylor(f6,h,'order',10));
a=sum(taylor(f7,h,'order',10));
v=sum(taylor(f9,h,'order',10));
q=sum(taylor(f10,h,'order',10));
q1=sum(taylor(f11,h,'order',10));
q2=sum(taylor(f12,h,'order',10));
q3=sum(taylor(f13,h,'order',10));
q4=sum(taylor(f14,h,'order',10));
q5=sum(taylor(f15,h,'order',10));
q6=sum(taylor(f16,h,'order',10));
v1 =0.50091382026531899391478548897399;
v2 =1.5931124176008341060884423751727;
V = sort([v1, v2 ]);
A = round(mean(V ));
[B,C] = rat((V(2)-A).^2 );
rBC = sqrt(sym(B)/sym(C ));
zq1=sym(A)-rBC
zq2=sym(A)+rBC
for i=0:10
xn=i*0.1
l1=z+[((r - 2)/r)*y-((2*r - 4)/(r - 1))*w-( 2/(r*(r - 1)))*v+((h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 - 53*r + 10))/(420*s*(r - s)*(s^2 - 3*s + 2)))*x-((h^3*(3*r + 21*s - 7*r*s - 21*r^2*s + 7*r^3*s + 7*r^2 + 9*r^3 - 4*r^4 - 5))/(420*r*(r - s)*(r - 1)))*m-((h^3*(r - 2)*(53*r + 91*s - 77*r*s - 21*r^2*s + 7*r^3*s + 21*r^2 + 5*r^3 - 3*r^4 - 86))/(420*(r - 1)*(s - 1)))*a-((h^3*(r - 2)*(24*r + 21*s - 70*r*s + 42*r^2*s - 7*r^3*s - 12*r^3 + 3*r^4 - 5))/(840*r*s))*diff(y,3)-((h^3*(7*s - 4*r + 14*r*s - 7*r^3*s + 2*r^3 + 3*r^4 - 19))/(840*(s - 2)))*p]
zz1 =simplify(subs(l1, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC,1,0,-2, 3*sin(xn),0.1]))
l2=h*b+[(((r - 3)/r)*y-((r - 4)/(r - 1))*w-(3/(r*(r - 1)))*v-((h^3*(- 9*r^5 + 54*r^4 - 72*r^3 - 72*r^2 + 117*r + 44))/(840*s*(r - s)*(s^2 - 3*s + 2)))*x+((h^3*(33*r + 84*s - 105*r*s - 105*r^2*s + 105*r^3*s - 21*r^4*s + 33*r^2 + 33*r^3 - 51*r^4 + 12*r^5 + 44))/(840*r*(r - s)*(r^2 - 3*r + 2)))*m-((h^3*(959*r*s - 812*s - 842*r - 105*r^2*s - 105*r^3*s + 21*r^4*s + 33*r^2 + 33*r^3 + 33*r^4 - 9*r^5 + 856))/(840*(r - 1)*(s - 1)))*a+((h^3*(117*r + 84*s - 469*r*s + 462*r^2*s - 168*r^3*s + 21*r^4*s - 72*r^2 - 72*r^3 + 54*r^4 - 9*r^5 + 44))/(1680*r*s))*diff(y,3)+((h^3*(243*r + 252*s - 63*r*s - 42*r^2*s - 42*r^3*s + 21*r^4*s + 12*r^2 + 12*r^3 + 12*r^4 - 9*r^5 - 460))/(1680*(r - 2)*(s - 2)))*p)]
zz2 =simplify(subs(l2, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l3=h^2*k+[-(2/r)*y+(2/(r - 1))*w-(2/(r*(r - 1)))*v+((h^3*(r^5 - 6*r^4 + 8*r^3 + 8*r^2 + 8*r - 41))/(140*s*(r - s)*(s^2 - 3*s + 2)))*x+((h^3*(11*r - 35*s - 35*r*s - 35*r^2*s + 35*r^3*s - 7*r^4*s + 11*r^2 + 11*r^3 - 17*r^4 + 4*r^5 + 123))/(420*r*(r - s)*(r^2 - 3*r + 2)))*m-((h^3*(525*r*s - 539*s - 549*r - 35*r^2*s - 35*r^3*s + 7*r^4*s + 11*r^2 + 11*r^3 + 11*r^4 - 3*r^5 + 662))/(420*(r - 1)*(s - 1)))*a-((h^3*(24*r + 35*s + 126*r*s - 154*r^2*s + 56*r^3*s - 7*r^4*s + 24*r^2 + 24*r^3 - 18*r^4 + 3*r^5 - 123))/(840*r*s))*diff(y,3)+((h^3*(564*r + 567*s - 294*r*s - 14*r^2*s - 14*r^3*s + 7*r^4*s + 4*r^2 + 4*r^3 + 4*r^4 - 3*r^5 - 1011))/(840*(r - 2)*(s - 2)))*p]
zz3 =simplify(subs(l3, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l4=h*q+[((r - 1)/r)*y-((r - 2)/(r - 1))*w-(1/(r*(r - 1)))*v+((h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 - 53*r + 20))/(840*s*(r - s)*(s^2 - 3*s + 2)))*x-((h^3*(42*s - 9*r + 7*r*s - 28*r^2*s + 7*r^3*s + 2*r^2 + 13*r^3 - 4*r^4 - 20))/(840*r*(r - s)*(r - 2)))*m-((h^3*(30*r + 56*s - 63*r*s - 28*r^2*s + 7*r^3*s + 19*r^2 + 8*r^3 - 3*r^4 - 36))/(840*(s - 1)))*a-((h^3*(r - 1)*(33*r + 42*s - 105*r*s + 49*r^2*s - 7*r^3*s + 9*r^2 - 15*r^3 + 3*r^4 - 20))/(1680*r*s))*diff(y,3)+((h^3*(r - 1)*(9*r + 14*s - 21*r*s - 7*r^2*s + 7*r^3*s + 5*r^2 + r^3 - 3*r^4 - 8))/(1680*(r - 2)*(s - 2)))*p]
zz4 =simplify(subs(l4, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l5=h^2*q1+[ -(2/r)*y+(2/(r - 1))*w-( 2/(r*(r - 1)))*v +((h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 - 81*r + 38))/(420*s*(r - s)*(s^2 - 3*s + 2)))*x+((h^3*(11*r + 70*s - 35*r*s - 35*r^2*s + 35*r^3*s - 7*r^4*s + 11*r^2 + 11*r^3 - 17*r^4 + 4*r^5 - 38))/(420*r*(r - s)*(r^2 - 3*r + 2)))*m-((h^3*(245*r*s - 154*s - 164*r - 35*r^2*s - 35*r^3*s + 7*r^4*s + 11*r^2 + 11*r^3 + 11*r^4 - 3*r^5 + 116))/(420*(r - 1)*(s - 1)))*a-((h^3*(196*r*s - 70*s - 81*r - 154*r^2*s + 56*r^3*s - 7*r^4*s + 24*r^2 + 24*r^3 - 18*r^4 + 3*r^5 + 38))/(840*r*s))*diff(y,3)+((h^3*(56*r*s - 28*s - 31*r - 14*r^2*s - 14*r^3*s + 7*r^4*s + 4*r^2 + 4*r^3 + 4*r^4 - 3*r^5 + 18))/(840*(r - 2)*(s - 2)))*p]
zz5 =simplify(subs(l5, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l6=h*q2+[-((r - 1)/r)*y+( r/(r - 1))*w-( (2*r - 1)/(r*(r - 1)))*v+((h^3*r*(- 8*r^5 + 45*r^4 - 74*r^3 + 24*r^2 + 24*r - 11))/(840*s*(r - s)*(s^2 - 3*s + 2)))*x-((h^3*(22*r - 35*s - 70*r*s + 105*r^2*s - 28*r^3*s + 33*r^2 - 68*r^3 + 20*r^4 + 11))/(840*(r - s)*(r - 2)))*m+((h^3*r*(r + 21*s - 14*r*s - 49*r^2*s + 14*r^3*s + 12*r^2 + 23*r^3 - 8*r^4 - 10))/(840*(s - 1)))*a+((h^3*(r - 1)*(13*r + 35*s - 119*r*s + 77*r^2*s - 14*r^3*s + 37*r^2 - 37*r^3 + 8*r^4 - 11))/(1680*s))*diff(y,3)-((h^3*r*(r - 1)*(r + 7*s - 7*r*s - 21*r^2*s + 14*r^3*s + 5*r^2 + 9*r^3 - 8*r^4 - 3))/(1680*(r - 2)*(s - 2)))*p]
zz6 =simplify(subs(l6, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l7=h^2*q3+[-(2/r)*y+(2/(r - 1))*w-(2/(r*(r - 1)))*v+((h^3*(- 18*r^5 + 87*r^4 - 116*r^3 + 24*r^2 + 24*r - 11))/(420*s*(r - s)*(s^2 - 3*s + 2)))*x+((h^3*(11*r - 35*s - 35*r*s + 385*r^2*s - 385*r^3*s + 98*r^4*s + 11*r^2 - 269*r^3 + 298*r^4 - 80*r^5 + 11))/(420*r*(r - s)*(r^2 - 3*r + 2)))*m-((h^3*(11*r + 21*s - 35*r*s - 35*r^2*s + 105*r^3*s - 28*r^4*s + 11*r^2 + 11*r^3 - 59*r^4 + 18*r^5 - 10))/(420*(r - 1)*(s - 1)))*a-((h^3*(24*r + 35*s - 154*r*s + 266*r^2*s - 154*r^3*s + 28*r^4*s + 24*r^2 - 116*r^3 + 87*r^4 - 18*r^5 - 11))/(840*r*s))*diff(y,3)+((h^3*(4*r + 7*s - 14*r*s - 14*r^2*s + 56*r^3*s - 28*r^4*s + 4*r^2 + 4*r^3 - 31*r^4 + 18*r^5 - 3))/(840*(r - 2)*(s - 2)))*p]
zz7 =simplify(subs(l7, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l8=q4+[(((r - s)*(s - 1))/r)*y-((s*(r - s))/(r - 1))*w-((s*(s - 1))/(r*(r - 1)))*v+((h^3*(3*r^4 + 3*r^3*s - 18*r^3 + 3*r^2*s^2 - 18*r^2*s + 24*r^2 + 3*r*s^3 - 18*r*s^2 + 24*r*s + 24*r - 4*s^4 + 17*s^3 - 11*s^2 - 11*s - 11))/(840*(s - 2)))*x-((h^3*s*(s - 1)*(- 4*r^4 + 3*r^3*s + 17*r^3 + 3*r^2*s^2 - 18*r^2*s - 11*r^2 + 3*r*s^3 - 18*r*s^2 + 24*r*s - 11*r + 3*s^4 - 18*s^3 + 24*s^2 + 24*s - 11))/(840*r*(r^2 - 3*r + 2)))*m+((h^3*s*(3*r^5 - 7*r^4*s - 11*r^4 + 35*r^3*s - 11*r^3 + 35*r^2*s - 11*r^2 + 7*r*s^4 - 35*r*s^3 - 35*r*s^2 + 10*r - 3*s^5 + 11*s^4 + 11*s^3 + 11*s^2 - 10*s))/(840*(r - 1)))*a+((h^3*(s - 1)*(- 3*r^5 + 7*r^4*s + 18*r^4 - 56*r^3*s - 24*r^3 + 154*r^2*s - 24*r^2 - 7*r*s^4 + 56*r*s^3 - 154*r*s^2 + 11*r + 3*s^5 - 18*s^4 + 24*s^3 + 24*s^2 - 11*s))/(1680*r))*diff(y,3)-((h^3*s*(s - 1)*(3*r^5 - 7*r^4*s - 4*r^4 + 14*r^3*s - 4*r^3 + 14*r^2*s - 4*r^2 + 7*r*s^4 - 14*r*s^3 - 14*r*s^2 + 3*r - 3*s^5 + 4*s^4 + 4*s^3 + 4*s^2 - 3*s))/(1680*(r - 2)*(s - 2)))*p]
zz8 =simplify(subs(l8, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l9=h*q5+[((r - 2*s + 1)/r)*y-((r - 2*s)/(r - 1))*w-((2*s - 1)/(r*(r - 1)))*v+((h^3*(6*r^5*s - 3*r^5 - 36*r^4*s + 18*r^4 + 48*r^3*s - 24*r^3 + 48*r^2*s - 24*r^2 - 42*r*s^5 + 210*r*s^4 - 280*r*s^3 + 48*r*s + 11*r + 28*s^6 - 126*s^5 + 140*s^4 - 22*s))/(840*s*(r - s)*(s^2 - 3*s + 2)))*x-((h^3*(- 8*r^5*s + 4*r^5 + 14*r^4*s^2 + 27*r^4*s - 17*r^4 - 70*r^3*s^2 + 13*r^3*s + 11*r^3 + 70*r^2*s^2 - 57*r^2*s + 11*r^2 + 70*r*s^2 - 57*r*s + 11*r - 14*s^6 + 84*s^5 - 140*s^4 + 70*s^2 - 22*s))/(840*r*(r - s)*(r^2 - 3*r + 2)))*m-((h^3*(- 6*r^5*s + 3*r^5 + 14*r^4*s^2 + 15*r^4*s - 11*r^4 - 70*r^3*s^2 + 57*r^3*s - 11*r^3 - 70*r^2*s^2 + 57*r^2*s - 11*r^2 - 28*r*s^5 + 140*r*s^4 - 70*r*s^2 + r*s + 10*r + 14*s^6 - 56*s^5 + 42*s^2 - 20*s))/(840*(r - 1)*(s - 1)))*a+((h^3*(- 6*r^5*s + 3*r^5 + 14*r^4*s^2 + 29*r^4*s - 18*r^4 - 112*r^3*s^2 + 8*r^3*s + 24*r^3 + 308*r^2*s^2 - 202*r^2*s + 24*r^2 - 28*r*s^5 + 210*r*s^4 - 560*r*s^3 + 308*r*s^2 - 13*r*s - 11*r + 14*s^6 - 84*s^5 + 140*s^4 - 70*s^2 + 22*s))/(1680*r*s))*diff(y,3)+((h^3*(- 6*r^5*s + 3*r^5 + 14*r^4*s^2 + r^4*s - 4*r^4 - 28*r^3*s^2 + 22*r^3*s - 4*r^3 - 28*r^2*s^2 + 22*r^2*s - 4*r^2 - 28*r*s^5 + 70*r*s^4 - 28*r*s^2 + r*s + 3*r + 14*s^6 - 28*s^5 + 14*s^2 - 6*s))/(1680*(r - 2)*(s - 2)))*p]
zz9 =simplify(subs(l9, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l10=h^2*q6+[-(2/r)*y+(2/(r - 1))*w-(2/(r*(r - 1)))*v+((h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 - 105*r*s^4 + 420*r*s^3 - 420*r*s^2 + 24*r + 84*s^5 - 315*s^4 + 280*s^3 - 11))/(420*s*(r - s)*(s^2 - 3*s + 2)))*x+((h^3*(4*r^5 - 7*r^4*s - 17*r^4 + 35*r^3*s + 11*r^3 - 35*r^2*s + 11*r^2 - 35*r*s + 11*r + 21*s^5 - 105*s^4 + 140*s^3 - 35*s + 11))/(420*r*(r - s)*(r^2 - 3*r + 2)))*m-((h^3*(- 3*r^5 + 7*r^4*s + 11*r^4 - 35*r^3*s + 11*r^3 - 35*r^2*s + 11*r^2 - 35*r*s^4 + 140*r*s^3 - 35*r*s + 11*r + 21*s^5 - 70*s^4 + 21*s - 10))/(420*(r - 1)*(s - 1)))*a-((h^3*(3*r^5 - 7*r^4*s - 18*r^4 + 56*r^3*s + 24*r^3 - 154*r^2*s + 24*r^2 + 35*r*s^4 - 210*r*s^3 + 420*r*s^2 - 154*r*s + 24*r - 21*s^5 + 105*s^4 - 140*s^3 + 35*s - 11))/(840*r*s))*diff(y,3)+((h^3*(- 3*r^5 + 7*r^4*s + 4*r^4 - 14*r^3*s + 4*r^3 - 14*r^2*s + 4*r^2 - 35*r*s^4 + 70*r*s^3 - 14*r*s + 4*r + 21*s^5 - 35*s^4 + 7*s - 3))/(840*(r - 2)*(s - 2)))*p]
zz10 =simplify(subs(l10, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l11=h*diff(y)+[((r + 1)/r)*y-(r/(r - 1))*w+(1/(r*(r - 1)))*v-((h^3*r*(3*r^4 - 18*r^3 + 24*r^2 + 24*r - 11))/(840*s*(r - s)*(s^2 - 3*s + 2)))*x-((h^3*(11*r - 35*s - 35*r*s + 35*r^2*s - 7*r^3*s + 11*r^2 - 17*r^3 + 4*r^4 + 11))/(840*(r - s)*(r^2 - 3*r + 2)))*m+((h^3*r*(11*r + 21*s - 35*r*s - 35*r^2*s + 7*r^3*s + 11*r^2 + 11*r^3 - 3*r^4 - 10))/(840*(r - 1)*(s - 1)))*a+((h^3*(24*r + 35*s - 154*r*s + 56*r^2*s - 7*r^3*s + 24*r^2 - 18*r^3 + 3*r^4 - 11))/(1680*s))*diff(y,3)-((h^3*r*(4*r + 7*s - 14*r*s - 14*r^2*s + 7*r^3*s + 4*r^2 + 4*r^3 - 3*r^4 - 3))/(1680*(r - 2)*(s - 2)))*p]
zz11 =simplify(subs(l11, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
l12=h^2*diff(y,2)+[-(2/r)*y+(2/(r - 1))*w-(2/(r*(r - 1)))*v+((h^3*(3*r^5 - 18*r^4 + 24*r^3 + 24*r^2 + 24*r - 11))/(420*s*(r - s)*(s^2 - 3*s + 2)))*x+((h^3*(11*r - 35*s - 35*r*s - 35*r^2*s + 35*r^3*s - 7*r^4*s + 11*r^2 + 11*r^3 - 17*r^4 + 4*r^5 + 11))/(420*r*(r - s)*(r^2 - 3*r + 2)))*m-((h^3*(11*r + 21*s - 35*r*s - 35*r^2*s - 35*r^3*s + 7*r^4*s + 11*r^2 + 11*r^3 + 11*r^4 - 3*r^5 - 10))/(420*(r - 1)*(s - 1)))*a-((h^3*(24*r + 35*s - 154*r*s - 154*r^2*s + 56*r^3*s - 7*r^4*s + 24*r^2 + 24*r^3 - 18*r^4 + 3*r^5 - 11))/(840*r*s))*diff(y,3)+((h^3*(4*r + 7*s - 14*r*s - 14*r^2*s - 14*r^3*s + 7*r^4*s + 4*r^2 + 4*r^3 + 4*r^4 - 3*r^5 - 3))/(840*(r - 2)*(s - 2)))*p]
zz12 =simplify(subs(l12, [r,s,y,diff(y),diff(y,2),diff(y,3),h], [sym(A)-rBC, sym(A)+rBC ,1,0,-2, 3*sin(xn),0.1]))
lllll=solve([zz1,zz2,zz3,zz4,zz5,zz6,zz7,zz8,zz9,zz10,zz11,zz12])
end

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