Unable to meet the tolerance without using more than 1666 mesh points.

Question

Syed Mohiuddin 2023-1-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1891207-unable-to-meet-the-tolerance-without-using-more-than-1666-mesh-points

评论： Torsten 2023-1-11

采纳的回答： Torsten

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I have a coupled non-linear differential equations

(d^2 f)/(dy^2 )+m2*g2*dB/dy-2*i*R2*g1*f - g3*G1*y - R4*g1 = 0

(d^2 B)/(dy^2 )+t4/(1-i*H1)*df/dy=0

(d^2 T)/(dy^2 )-1/2*g4*G1*PR*(f+ ̅f)+ER*PR*[g5*(df/dy*d ̅f/dy)+g6*m2*(dB/dy*dB̅/dy)]=0, where ̅f is conjugate of f and B̅ is conjugate of B

Boundary conditions are

f=0 at y=0

f=C1 at y=1

And

dB/dy-(t4/(P1* (1-i*H1 ) ))* B=0 at y=0

dB/dy+(t4/(P2 (1-i*H1 ) ))* B=0 at y=1

and

T=0 at y=0

T=1 at y=1

I already got the solutions and graph for the first two equations with the help received from Torsen, but now i have extended the problem for three equations, when i run the program, i get an error "Unable to meet the tolerance without using more than 1666 mesh points", I tried using NMax but could not get the solution

Matlab programs

close all

clc

p=0.1;

P1=2;

P2=2;

b1=0.00021;

b2=0.000058;

S1=0.005;

S2=580000;

G1=2;

m2=20;

R1=997.1;

R2=3;

C1=0;

R3=4420;

H1=0.25;

K1=3;

R4=1;

PR=7.0;

ER= 2.0;

cf=4179;

cs=0.56;

K2=0.613;

K3=7.2;

t1=(1./((1-p).^2.5));

t2=(1-p)+(p.*(R3./R1));

t3=(1-p)+p.*((R3.*b2)./(R1.*b1));

S=(S2./S1);

t4=1-((3*(1-S).*p)./((2+S)+(1-S).*p));

t5=(1-p)+(p.*R3.*cs)./(R1.*cf);

t6=(1+2.*(K2./K3)+2.*p.*(1-K2./K3))./(1+2.*(K2./K3)-p.*(1-K2./K3));

g1=t2./t1;

g2=1/t1;

g3=t3./t1;

g4=t5./t6;

g5=t1./t6;

g6=1./(t4.*t6);

m1=(t4./(P1.*(1-1i.*H1)));

m2=(t4./(P2.*(1-1i.*H1)));

dydx=@(x,y)[y(4);

y(5);

y(6);

-m2.*g2.*y(4)+2.*1i.*R2.*g1.*y(1)+g3.*G1.*x+R4.*g1;

(-t4./(1-1i.*H1)).*y(3);

1/2.*g4.*G1.*PR.*(y(1)+conj(y(1)))-ER.*PR.*(g5.*(y(4).*conj(y(4))+g6.*m2.*(y(5).*conj(y(5)))))];

BC = @(ya,yb)[ya(1)-0;yb(1)-C1;ya(3)-0;yb(3)-1.0;ya(5)-m1.*ya(2);yb(5)+m2.*yb(2)];

yinit = [0.01;0.01;0.01;0.01;0.01;0.01];

solinit = bvpinit(linspace(0,1,50),yinit);

% options = bvpset('AbsTol',1e-6,'RelTol',1e-4,'stats','on','Nmax',1000);

options = bvpset('AbsTol',1e-6);

% options = bvpset('RelTol',1e-4);

%options = bvpset('stats','on');

%options = bvpset('Nmax',1000);

U1 = bvp4c(dydx,BC,solinit,options);

hold on

plot(U1.x,real(U1.y(3,:)),'b','linewidth',1.5)

plot(U1.x,imag(U1.y(3,:)),'r','linewidth',1.5)

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Syed Mohiuddin 2023-1-10

I use R2016b, for the previous question also i did not get the option to accept the answer, please provide the option for the previous question too. Thank you