MATLAB: I want solve y”’=3sin(xn),y(0)=1,y'(0)=0,y”(0)=-2 ,the analyic solution 3cos(xn)+((xn)^2/2)-2 by hybrid block method i have the system of the block method in which i will apply this differential equation the broblem the numerical solution not

differential equations

clear all 
clc
syms x h r s  yn(xni)   yn(xn)  fn(xn) v(xn) w(xn) p(xn) xx(xn) a(xn) yn2 
 q1=xn+2*h;
 q2=xn+h;
 q3=xn+r*h;
 q4=xn+s*h;
 f1=yn(q1);
 f2=yn(q2);
 f3=diff(yn(q3),3);
 f4=diff(yn(q4),3);
 f5=diff(yn(q1),3);
 f6=diff(yn(q1));
 f7=diff(yn(q2),3);
 f8=diff(yn(q1),2);
 f9=yn(q3);
 f10=diff(yn(q2));
 f11=diff(yn(q2),2);
 f12=diff(yn(q3));
 f13=diff(yn(q3),2);
 f14=yn(q4);
 f15=diff(yn(q4));
 f16=diff(yn(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));
 xx=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((B)/(C ));
%r=sym(A)-rBC;
%s=sym(A)+rBC;
x1=0;xr=1;                  
J=10;                       
dx=(xr-x1)/J;
xn=0
ynn1 =-(- 1680*yn*r^4*s^3 + 5040*yn*r^4*s^2 - 3360*yn*r^4*s + 1680*yn*r^3*s^4 - 11760*yn*r^3*s^2 + 10080*yn*r^3*s - 5040*yn*r^2*s^4 + 11760*yn*r^2*s^3 - 6720*yn*r^2*s + 3360*yn*r*s^4 - 10080*yn*r*s^3 + 6720*yn*r*s^2)/(1680*r*s*(r - s)*(r^2 - 3*r + 2)*(s^2 - 3*s + 2))
W5=simplify(subs(ynn1, [r,s,fn,h,diff(yn(xn),3),diff(yn),diff(yn,2),yn],[(sym(A)-rBC),(sym(A)+rBC),3*sin(xn),0.1,3*sin(xn),0,-2,1]))
xn=0.025
yr =-(- 1680*v*r^4*s^3 + 5040*v*r^4*s^2 - 3360*v*r^4*s + 1680*v*r^3*s^4 - 11760*v*r^3*s^2 + 10080*v*r^3*s - 5040*v*r^2*s^4 + 11760*v*r^2*s^3 - 6720*v*r^2*s + 3360*v*r*s^4 - 10080*v*r*s^3 + 6720*v*r*s^2)/(1680*r*s*(r - s)*(r^2 - 3*r + 2)*(s^2 - 3*s + 2))
W3=simplify(subs(yr, [r,s,fn,h,diff(yn(xn),3),diff(yn),diff(yn,2),yn],[(sym(A)-rBC),(sym(A)+rBC),3*sin(xn),0.1,3*sin(xn),0,-2, 1]))
xn=0.05
y11 =-(- 1680*w*r^4*s^3 + 5040*w*r^4*s^2 - 3360*w*r^4*s + 1680*w*r^3*s^4 - 11760*w*r^3*s^2 + 10080*w*r^3*s - 5040*w*r^2*s^4 + 11760*w*r^2*s^3 - 6720*w*r^2*s + 3360*w*r*s^4 - 10080*w*r*s^3 + 6720*w*r*s^2)/(1680*r*s*(r - s)*(r^2 - 3*r + 2)*(s^2 - 3*s + 2))
W2=simplify(subs(y11, [r,s,fn,h,diff(yn(xn),3),diff(yn),diff(yn,2),yn],[(sym(A)-rBC),(sym(A)+rBC),3*sin(xn),0.1,3*sin(xn),0,-2,   0.9983]))
xn=0.075
ys =(6720*s^3*yn - 16800*s^4*yn + 13440*s^5*yn - 3360*s^6*yn - 6720*s^3*v + 16800*s^4*v - 13440*s^5*v + 3360*s^6*v - 13440*r*s^2*yn + 6720*r^2*s*yn + 23520*r*s^3*yn - 10080*r^3*s*yn - 1680*r*s^4*yn + 3360*r^4*s*yn - 6720*r*s^4*w - 13440*r*s^5*yn + 10080*r*s^5*w + 5040*r*s^6*yn - 3360*r*s^6*w + 6720*r*s^2*v - 13440*r*s^3*v + 5040*r*s^4*v + 3360*r*s^5*v - 1680*r*s^6*v + 44*fn*h^3*s^3 - 206*fn*h^3*s^4 + 232*fn*h^3*s^5 + 98*fn*h^3*s^6 - 336*fn*h^3*s^7 + 222*fn*h^3*s^8 - 60*fn*h^3*s^9 + 6*fn*h^3*s^10 - 44*m*h^3*s^3 + 206*m*h^3*s^4 - 232*m*h^3*s^5 - 98*m*h^3*s^6 + 336*m*h^3*s^7 - 222*m*h^3*s^8 + 60*m*h^3*s^9 - 6*m*h^3*s^10 + 3360*r^2*s^2*yn - 33600*r^2*s^3*yn + 18480*r^3*s^2*yn + 13440*r^2*s^3*w + 28560*r^2*s^4*yn - 6720*r^3*s^2*w - 3360*r^3*s^3*yn - 8400*r^4*s^2*yn - 16800*r^2*s^4*w - 3360*r^2*s^5*yn + 3360*r^3*s^3*w - 8400*r^3*s^4*yn + 3360*r^4*s^2*w + 6720*r^4*s^3*yn + 1680*r^2*s^5*w - 1680*r^2*s^6*yn + 6720*r^3*s^4*w + 3360*r^3*s^5*yn - 5040*r^4*s^3*w - 1680*r^4*s^4*yn + 1680*r^2*s^6*w - 3360*r^3*s^5*w + 1680*r^4*s^4*w - 3360*r^2*s^2*v + 8400*r^2*s^3*v - 6720*r^2*s^4*v + 1680*r^2*s^5*v + 118*fn*h^3*r^2*s^2 - 1836*fn*h^3*r^2*s^3 + 929*fn*h^3*r^3*s^2 + 2927*fn*h^3*r^2*s^4 + 486*fn*h^3*r^3*s^3 - 1491*fn*h^3*r^4*s^2 - 160*a*h^3*r^2*s^3 + 80*a*h^3*r^3*s^2 - 224*fn*h^3*r^2*s^5 - 4151*fn*h^3*r^3*s^4 + 2450*fn*h^3*r^4*s^3 + 420*fn*h^3*r^5*s^2 + 288*a*h^3*r^2*s^4 + 48*a*h^3*r^3*s^3 - 128*a*h^3*r^4*s^2 + 6*p*h^3*r^2*s^3 - 3*p*h^3*r^3*s^2 - 2051*fn*h^3*r^2*s^6 + 3822*fn*h^3*r^3*s^5 - 105*fn*h^3*r^4*s^4 - 1610*fn*h^3*r^5*s^3 + 212*fn*h^3*r^6*s^2 + 260*a*h^3*r^2*s^5 - 816*a*h^3*r^3*s^4 + 516*a*h^3*r^4*s^3 - 44*a*h^3*r^5*s^2 - 13*p*h^3*r^2*s^4 - 4*p*h^3*r^3*s^3 + 7*p*h^3*r^4*s^2 + 1236*fn*h^3*r^2*s^7 - 735*fn*h^3*r^3*s^6 - 1596*fn*h^3*r^4*s^5 + 1211*fn*h^3*r^5*s^4 + 170*fn*h^3*r^6*s^3 - 115*fn*h^3*r^7*s^2 - 182*a*h^3*r^2*s^6 + 526*a*h^3*r^3*s^5 - 550*a*h^3*r^4*s^4 + 250*a*h^3*r^5*s^3 - 44*a*h^3*r^6*s^2 - 14*p*h^3*r^2*s^5 + 49*p*h^3*r^3*s^4 - 28*p*h^3*r^4*s^3 - 217*fn*h^3*r^2*s^8 - 272*fn*h^3*r^3*s^7 + 749*fn*h^3*r^4*s^6 - 112*fn*h^3*r^5*s^5 - 297*fn*h^3*r^6*s^4 + 58*fn*h^3*r^7*s^3 + 15*fn*h^3*r^8*s^2 - 448*a*h^3*r^2*s^7 + 266*a*h^3*r^3*s^6 + 302*a*h^3*r^4*s^5 - 102*a*h^3*r^5*s^4 - 198*a*h^3*r^6*s^3 + 68*a*h^3*r^7*s^2 + 21*p*h^3*r^2*s^6 - 42*p*h^3*r^3*s^5 + 21*p*h^3*r^4*s^4 + 93*fn*h^3*r^3*s^8 - 84*fn*h^3*r^4*s^7 - 77*fn*h^3*r^5*s^6 + 76*fn*h^3*r^6*s^5 + 13*fn*h^3*r^7*s^4 - 12*fn*h^3*r^8*s^3 + 248*a*h^3*r^2*s^8 - 238*a*h^3*r^4*s^6 - 202*a*h^3*r^5*s^5 + 346*a*h^3*r^6*s^4 - 62*a*h^3*r^7*s^3 - 12*a*h^3*r^8*s^2 + 28*p*h^3*r^2*s^7 - 21*p*h^3*r^3*s^6 - 21*p*h^3*r^5*s^4 + 28*p*h^3*r^6*s^3 - 7*p*h^3*r^7*s^2 + 3*fn*h^3*r^2*s^10 - 10*fn*h^3*r^3*s^9 + 7*fn*h^3*r^4*s^8 + 7*fn*h^3*r^6*s^6 - 10*fn*h^3*r^7*s^5 + 3*fn*h^3*r^8*s^4 - 124*a*h^3*r^3*s^8 + 112*a*h^3*r^4*s^7 + 98*a*h^3*r^5*s^6 - 90*a*h^3*r^6*s^5 - 26*a*h^3*r^7*s^4 + 18*a*h^3*r^8*s^3 - 31*p*h^3*r^2*s^8 + 21*p*h^3*r^4*s^6 + 42*p*h^3*r^5*s^5 - 49*p*h^3*r^6*s^4 + 4*p*h^3*r^7*s^3 + 3*p*h^3*r^8*s^2 - 6*a*h^3*r^2*s^10 + 20*a*h^3*r^3*s^9 - 14*a*h^3*r^4*s^8 - 14*a*h^3*r^6*s^6 + 20*a*h^3*r^7*s^5 - 6*a*h^3*r^8*s^4 + 31*p*h^3*r^3*s^8 - 28*p*h^3*r^4*s^7 - 21*p*h^3*r^5*s^6 + 14*p*h^3*r^6*s^5 + 13*p*h^3*r^7*s^4 - 6*p*h^3*r^8*s^3 + 3*p*h^3*r^2*s^10 - 10*p*h^3*r^3*s^9 + 7*p*h^3*r^4*s^8 + 7*p*h^3*r^6*s^6 - 10*p*h^3*r^7*s^5 + 3*p*h^3*r^8*s^4 + 44*m*h^3*r^2*s^2 - 250*m*h^3*r^2*s^3 + 44*m*h^3*r^3*s^2 + 438*m*h^3*r^2*s^4 + 30*m*h^3*r^3*s^3 - 68*m*h^3*r^4*s^2 - 302*m*h^3*r^2*s^5 - 262*m*h^3*r^3*s^4 + 142*m*h^3*r^4*s^3 + 16*m*h^3*r^5*s^2 + 70*m*h^3*r^2*s^6 + 258*m*h^3*r^3*s^5 - 66*m*h^3*r^4*s^4 - 40*m*h^3*r^5*s^3 - 70*m*h^3*r^3*s^6 - 22*m*h^3*r^4*s^5 + 32*m*h^3*r^5*s^4 + 14*m*h^3*r^4*s^6 - 8*m*h^3*r^5*s^5 - 162*xx*h^3*r^2*s^2 + 70*xx*h^3*r^3*s^2 + 280*xx*h^3*r^2*s^4 - 420*xx*h^3*r^3*s^4 + 168*xx*h^3*r^5*s^2 - 98*xx*h^3*r^2*s^6 + 196*xx*h^3*r^3*s^5 + 140*xx*h^3*r^4*s^4 - 168*xx*h^3*r^6*s^2 + 24*xx*h^3*r^2*s^7 - 84*xx*h^3*r^4*s^5 + 54*xx*h^3*r^7*s^2 - 8*xx*h^3*r^3*s^7 + 14*xx*h^3*r^4*s^6 - 6*xx*h^3*r^8*s^2 - 88*fn*h^3*r*s^2 + 44*fn*h^3*r^2*s + 250*fn*h^3*r*s^3 - 162*fn*h^3*r^3*s + 605*fn*h^3*r*s^4 + 70*fn*h^3*r^4*s - 2188*fn*h^3*r*s^5 + 168*fn*h^3*r^5*s + 80*a*h^3*r*s^4 + 2009*fn*h^3*r*s^6 - 168*fn*h^3*r^6*s - 208*a*h^3*r*s^5 - 3*p*h^3*r*s^4 - 544*fn*h^3*r*s^7 + 54*fn*h^3*r^7*s + 84*a*h^3*r*s^6 + 10*p*h^3*r*s^5 - 105*fn*h^3*r*s^8 - 6*fn*h^3*r^8*s - 7*p*h^3*r*s^6 + 70*fn*h^3*r*s^9 + 112*a*h^3*r*s^8 - 9*fn*h^3*r*s^10 - 80*a*h^3*r*s^9 - 7*p*h^3*r*s^8 + 12*a*h^3*r*s^10 + 10*p*h^3*r*s^9 - 3*p*h^3*r*s^10 + 44*m*h^3*r*s^2 - 250*m*h^3*r*s^3 + 438*m*h^3*r*s^4 - 302*m*h^3*r*s^5 + 70*m*h^3*r*s^6 + 44*xx*h^3*r*s^2 - 44*xx*h^3*r^2*s + 162*xx*h^3*r^3*s - 70*xx*h^3*r^4*s - 112*xx*h^3*r*s^5 - 168*xx*h^3*r^5*s + 84*xx*h^3*r*s^6 + 168*xx*h^3*r^6*s - 16*xx*h^3*r*s^7 - 54*xx*h^3*r^7*s + 6*xx*h^3*r^8*s)/(1680*r*s*(r - s)*(r^2 - 3*r + 2)*(s^2 - 3*s + 2))
W4=simplify(subs(ys, [r,s,fn,h,diff(yn(xn),3),diff(yn),diff(yn,2),yn],[(sym(A)-rBC),(sym(A)+rBC),3*sin(xn),0.1,3*sin(xn),0,-2,0.9883]))
for i=1:10
xn=(i)*0.1
y22_(i,1) =-(13440*s^2*yn - 20160*s^3*yn + 6720*s^4*yn - 13440*s^2*v + 20160*s^3*v - 6720*s^4*v + 80*fn*h^3*s - 80*m*h^3*s - 6720*r*s^2*yn + 26880*r^2*s*yn + 26880*r*s^2*w + 33600*r*s^3*yn - 26880*r^2*s*w - 16800*r^3*s*yn - 40320*r*s^3*w - 13440*r*s^4*yn + 26880*r^3*s*w + 3360*r^4*s*yn + 13440*r*s^4*w - 6720*r^4*s*w - 13440*r*s^2*v - 6720*r^2*s*v - 3360*r*s^3*v+ 3360*r*s^4*v + 544*fn*h^3*r^2 - 868*fn*h^3*r^3 + 308*fn*h^3*r^4 + 336*fn*h^3*r^5 - 336*fn*h^3*r^6 + 108*fn*h^3*r^7 - 12*fn*h^3*r^8 - 544*xx*h^3*r^2 + 868*xx*h^3*r^3 - 308*xx*h^3*r^4 - 336*xx*h^3*r^5 + 336*xx*h^3*r^6 - 108*xx*h^3*r^7 + 12*xx*h^3*r^8 - 456*fn*h^3*s^2 + 544*fn*h^3*s^3 - 168*fn*h^3*s^4 + 456*m*h^3*s^2 - 544*m*h^3*s^3 + 168*m*h^3*s^4 - 23520*r^2*s^2*yn + 13440*r^2*s^2*w - 11760*r^2*s^3*yn + 21840*r^3*s^2*yn+ 26880*r^2*s^3*w + 8400*r^2*s^4*yn - 33600*r^3*s^2*w - 3360*r^3*s^3*yn - 5040*r^4*s^2*yn - 13440*r^2*s^4*w + 3360*r^3*s^3*w - 1680*r^3*s^4*yn + 10080*r^4*s^2*w + 1680*r^4*s^3*yn + 3360*r^3*s^4*w - 3360*r^4*s^3*w + 10080*r^2*s^2*v - 3360*r^2*s^3*v - 13440*r*s*yn+ 13440*r*s*v - 80*fn*h^3*r + 80*xx*h^3*r - 1674*fn*h^3*r^2*s^2 + 4536*fn*h^3*r^2*s^3 - 2030*fn*h^3*r^3*s^2 - 160*a*h^3*r^2*s^2 - 1666*fn*h^3*r^2*s^4 - 2898*fn*h^3*r^3*s^3 + 3724*fn*h^3*r^4*s^2 + 6144*a*h^3*r^2*s^3 - 5888*a*h^3*r^3*s^2 + 6*p*h^3*r^2*s^2 + 1470*fn*h^3*r^3*s^4 + 378*fn*h^3*r^4*s^3 - 2044*fn*h^3*r^5*s^2 - 2688*a*h^3*r^2*s^4 - 688*a*h^3*r^3*s^3 + 3464*a*h^3*r^4*s^2 + 56*p*h^3*r^2*s^3 - 70*p*h^3*r^3*s^2 - 672*fn*h^3*r^4*s^4 + 378*fn*h^3*r^5*s^3 + 428*fn*h^3*r^6*s^2 + 1260*a*h^3*r^3*s^4 - 1584*a*h^3*r^4*s^3 + 412*a*h^3*r^5*s^2 + 14*p*h^3*r^2*s^4 + 42*p*h^3*r^3*s^3 - 56*p*h^3*r^4*s^2 + 154*fn*h^3*r^5*s^4 - 166*fn*h^3*r^6*s^3 - 6*fn*h^3*r^7*s^2 + 140*a*h^3*r^4*s^4 + 208*a*h^3*r^5*s^3 - 484*a*h^3*r^6*s^2 - 70*p*h^3*r^3*s^4 + 70*p*h^3*r^4*s^3 - 14*fn*h^3*r^6*s^4 + 20*fn*h^3*r^7*s^3 - 6*fn*h^3*r^8*s^2 - 196*a*h^3*r^5*s^4 + 208*a*h^3*r^6*s^3 + 12*a*h^3*r^7*s^2 - 42*p*h^3*r^5*s^3 + 56*p*h^3*r^6*s^2 + 28*a*h^3*r^6*s^4 - 40*a*h^3*r^7*s^3 + 12*a*h^3*r^8*s^2 + 42*p*h^3*r^5*s^4 - 42*p*h^3*r^6*s^3 - 6*p*h^3*r^7*s^2 - 14*p*h^3*r^6*s^4 + 20*p*h^3*r^7*s^3 - 6*p*h^3*r^8*s^2 - 412*m*h^3*r^2*s^2 + 464*m*h^3*r^2*s^3 + 148*m*h^3*r^3*s^2 - 140*m*h^3*r^2*s^4 - 376*m*h^3*r^3*s^3 + 148*m*h^3*r^4*s^2 + 140*m*h^3*r^3*s^4 + 16*m*h^3*r^4*s^3 - 48*m*h^3*r^5*s^2 - 28*m*h^3*r^4*s^4 + 16*m*h^3*r^5*s^3 - 88*fn*h^3*r*s + 88*m*h^3*r*s + 2064*fn*h^3*r*s^2 - 1740*fn*h^3*r^2*s - 2792*fn*h^3*r*s^3 + 4326*fn*h^3*r^3*s + 2752*a*h^3*r*s^2 - 2752*a*h^3*r^2*s + 896*fn*h^3*r*s^4 - 3738*fn*h^3*r^4*s - 4288*a*h^3*r*s^3 + 4448*a*h^3*r^3*s + 76*p*h^3*r*s^2 - 76*p*h^3*r^2*s + 1176*fn*h^3*r^5*s + 1456*a*h^3*r*s^4 - 1712*a*h^3*r^4*s - 104*p*h^3*r*s^3 + 98*p*h^3*r^3*s + 88*fn*h^3*r^6*s - 88*a*h^3*r^5*s + 28*p*h^3*r*s^4 - 14*p*h^3*r^4*s - 122*fn*h^3*r^7*s - 88*a*h^3*r^6*s + 18*fn*h^3*r^8*s + 136*a*h^3*r^7*s - 24*a*h^3*r^8*s - 14*p*h^3*r^7*s + 6*p*h^3*r^8*s - 412*m*h^3*r*s^2 + 88*m*h^3*r^2*s + 464*m*h^3*r*s^3 + 88*m*h^3*r^3*s - 140*m*h^3*r*s^4 - 136*m*h^3*r^4*s + 32*m*h^3*r^5*s)/(1680*r*s*(r - s)*(r^2 - 3*r + 2)*(s^2 - 3*s + 2))
W1_(i,1)=simplify(subs(y22_(i,1),[r,s,fn,h,diff(yn(xn),3),diff(yn(0),2),diff(yn(0)),yn(0)],[(sym(A)-rBC),(sym(A)+rBC),3*sin(xn),0.1,3*sin(xn),-2,0,1]))
dsolve(w1_(i,1))
end
%calculate the analytic solution
    for j=1:J+1
        xj=x1+(j-1)*dx;
       u_ex(j,1)=3*cos(xj)+((xj)^2/2)-2
        end

Best Answer

>> syms y(xn)
>> dy = diff(y)
dy(xn) =
diff(y(xn), xn)
>> d2y = diff(dy)
d2y(xn) =
diff(y(xn), xn, xn)
>> d3y = diff(d2y)
d3y(xn) =
diff(y(xn), xn, xn, xn)
>> eqn = [y(0)==1, dy(0)==0, d2y(0)==-2, d3y == 3*sin(xn)]
eqn(xn) =
[ y(0) == 1, subs(diff(y(xn), xn), xn, 0) == 0, subs(diff(y(xn), xn, xn), xn, 0) == -2, diff(y(xn), xn, xn, xn) == 3*sin(xn)]
>> dsolve(eqn)
ans =
3*cos(xn) + xn^2/2 - 2

Related Solutions

MATLAB: How to applay y”’+y’=0 , y(0)=y0=0, y'(0)=y01=1, y”(0)=y011=-2 in the following system where fn=y”’ i got this error Error using mupadengine/feval (line 157) MuPAD error: Error: Cannot differentiate the equation. [numeric::fsolve] Error in sym

Change

syms y

syms y(t)

MATLAB: When I run the program inaccurate results appear What is the problem

The best approach to this is likely not the vpasolve function, since it takes forever.

I have no idea of these are the ‘accurate’ results you want (I have no idea what that means), however you will get them much more quickly:

syms t y1 y2 y3 y4  yn11 yn1 yr yr11 yr111   yr v y(v) x
format longe
h=0.1;
r=1.7686999343761197980595002942562;   %1694/911=1.859495060373216e+00
x=0;
y0=0;
y01=0.25;
y011=0;
fn=-y01+y0.*y01.*y011;
fnr=-yr11+yr.*yr11.*yr111;
fn1=-yn1+y1.*yn1.*yn11;
fn2=-y3+y2.*y3.*y4;
eq1 =-y2-(r - 2)/r*y0+ 2/(r*(r - 1))*yr+ (2*r - 4)/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 23*r + 6))/(120*r)*fn+ (h.^3.*(- r^2 + 2*r + 3))/(60*r)*fnr -(h.^3.*(- r^3 + 4*r^2 + 9*r - 26))/60*fn1+ (h.^3.*(- r^3 + 2*r + 1))/120*fn2;
eq1 = simplifyFraction(eq1);
eq1d = vpa(eq1, 5)
eq2= -h.*y3 -(r - 3)/r*y0+ 3/(r*(r - 1))*yr+ (r - 4)/(r - 1)*y1 -(h.^3.*(3*r^4 - 24*r^3 + 66*r^2 - 67*r + 12))/(240*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r - 4))/(40*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- 3*r^4 + 15*r^3 + 15*r^2 - 137*r + 116))/(120*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 3*r - 12))/(80*(r - 2))*fn2;
eq2 = simplifyFraction(eq2);
eq2d = vpa(eq2, 5)
eq3=-h.^2.*y4+2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1+ (h.^3.*(- r^4 + 8*r^3 - 22*r^2 + 18*r + 5))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 - 75*r + 77))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 42*r - 81))/(120*(r - 2))*fn2;
eq3 = simplifyFraction(eq3);
eq3d = vpa(eq3, 5)
eq4=-h.*yn1 -(r - 1)/r*y0+ 1/(r*(r - 1))*yr+ (r - 2)/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 21*r + 6))/(240*r)*fn+ (h.^3.*(- r^2 + 2*r + 3))/(120*r)*fnr -(h.^3.*(- r^3 + 4*r^2 + 9*r - 8))/120*fn1 -(h.^3.*(r^3 - 2*r + 1))/240*fn2;
eq4 = simplifyFraction(eq4);
eq4d = vpa(eq4, 5)
eq5=-h.^2.*yn11+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 28*r + 10))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r - 10))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 - 35*r + 22))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 - 8*r + 4))/(120*(r - 2))*fn2;
eq5 = simplifyFraction(eq5);
eq5d = vpa(eq5, 5)
eq6=-h.*yr11+ (r - 1)/r*y0+ (2*r - 1)/(r*(r - 1))*yr -r/(r - 1)*y1+ (h.^3.*(2*r^4 - 13*r^3 + 28*r^2 - 22*r + 5))/240*fn+ (h.^3.*(4*r^3 - 15*r^2 + 10*r + 5))/(120*(r - 2))*fnr+ (h.^3.*r*(- 2*r^3 + 7*r^2 + 2*r - 3))/120*fn1+ (h.^3.*r*(2*r^4 - 5*r^3 + 2*r^2 + 2*r - 1))/(240*(r - 2))*fn2;
eq6 = simplifyFraction(eq6);
eq6d = vpa(eq6, 5)
eq7=-h.^2.*yr111+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1+ (h.^3.*(4*r^4 - 22*r^3 + 38*r^2 - 22*r + 5))/(120*r)*fn -(h.^3.*(- 14*r^4 + 55*r^3 - 55*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(4*r^4 - 15*r^3 + 5*r^2 + 5*r - 3))/(60*(r - 1))*fn1+ (h.^3.*(4*r^4 - 8*r^3 + 2*r^2 + 2*r - 1))/(120*(r - 2))*fn2;
eq7 = simplifyFraction(eq7);
eq7d = vpa(eq7, 5)
eq8=-h.*y01 -(r + 1)/r*y0 -1/(r*(r - 1))*yr+ r/(r - 1)*y1+ (h.^3.*(r^3 - 8*r^2 + 22*r - 5))/240*fn+ (h.^3.*(r^3 - 5*r^2 + 5*r + 5))/(120*(r^2 - 3*r + 2))*fnr+ (h.^3.*r*(- r^3 + 5*r^2 + 5*r - 3))/(120*(r - 1))*fn1 -(h.^3.*r*(- r^3 + 2*r^2 + 2*r - 1))/(240*(r - 2))*fn2;
eq8 = simplifyFraction(eq8);
eq8d = vpa(eq8, 5)
eq9 =-h.^2.*y011+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 + 22*r - 5))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 + 5*r - 3))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 2*r - 1))/(120*(r - 2))*fn2;
eq9 = simplifyFraction(eq9);
eq9d = vpa(eq9, 5)
eqsfcn = matlabFunction([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9], 'Vars',{[y1,y2,y3,y4,yn1,yn11,yr,yr11,yr111]})
eqsol = fsolve(eqsfcn, rand(1,9))
eqsolc = num2cell(eqsol);
[y1,y2,y3,y4,yn1,yn11,yr,yr11,yr111] = eqsolc{:}

I used the simplifyFraction function to do just that with your equations, then the fsolve function to do the actual calculations. These changes make it significantly more efficient.

The results I got are:

y1 =
     2.495835158216658e-02
y2 =
     4.966725033036157e-02
y3 =
     2.450145921764798e-01
y4 =
    -4.970810349993776e-02
yn1 =
     2.487509121241510e-01
yn11 =
    -2.496352514349295e-02
yr =
     4.398727143758653e-02
yr11 =
     2.460985502335340e-01
yr111 =
    -4.401564490668385e-02

You must be certain your equations are written as you want them to be in order to get ‘accurate’ values. We have no control over that.

Experiment to get the results you want.

Best Answer

Related Solutions

MATLAB: How to applay y”’+y’=0 , y(0)=y0=0, y'(0)=y01=1, y”(0)=y011=-2 in the following system where fn=y”’ i got this error Error using mupadengine/feval (line 157) MuPAD error: Error: Cannot differentiate the equation. [numeric::fsolve] Error in sym

MATLAB: When I run the program inaccurate results appear What is the problem

Related Question