I am trying to solve 3rd order ode by RK45, but I did not get solution and plot, kindly fix my issues

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Asaigeethan P
Asaigeethan P 2021-11-6
评论： Asaigeethan P 2021-11-11
clear all;
clc;
close all;
h1(1)=0; % initial condition
y(1)=1; % initial condition
z(1)=-1; % initial condition
we=4;
k=0.5;
n=0.2;
B=0.5;
pr=2;
sc=1.2;
L=0.5;
p=1; % h5 value
q=1; % h51 value
r=0.1; % h6 value
s=L.*r; % h7 value
a=0;
b=5;
m=100;
h=(b-a)/m;
x=a:h:b;
i=0;
nr1=(y.^2-h1*z-2*k*z*(1+we.^2*z^2).^((n-1)/2)-k*(n-1)*(1+we.^2*z^2).^((n-3)/2)+B*y);
dr1=(1+2*k*x).*(1+we.^2*z.^2).^((n-1)/2)+(n-1).*we.^2*z.^2.*(1+2*k*x).*((1+we.^2*z.^2).^(n-3)/2);
nr2=-2*k*p-(pr).*p*x;
dr2=1+2*k*x;
nr3=L.*r*(1-r).^2-s.*x-(2./sc).*k.*s;
dr3=1./sc;
f1=@(x,y,z) (nr1./dr1);
f2=@(x,p,q) (nr2./dr2);
f3=@(x,r,s) (nr3./dr3);
for i=i+1;
xx(i+1,:)=x;
%RK45
k1=h*f1(x,y(i));
k2=h*f1(x+h/4 , y(i)+(1/4)*k1);
k3=h*f1(x+(3*h/8),y(i)+(3/32)*k1+(9/32)*k2);
k4=h*f1(x+(12*h/13),y(i)+(1932/2197)*k1-(7200/2197)*k2+(7296/2197)*k3);
k5=h*f1(x+h,y(i)+(439/216)*k1-8*k2+(3680513)*k3-(845/4104)*k4);
k6=h*f1(x+0.5*h,y(i)-(8/27)*k1+2*k2-(3544/2565)*k3+(1859/4104)*k4-(11/40)*k5);
y(i+1,:)=(y(i,:)+((16/135)*k1+(6656/12825)*k3+(28561/56430)*k4-(9/50)*k5+(2/55)*k6));
erro(i+1,:)=((1/360)*k1-(128/4275)*k3+(2197/75240)*k4+(1/50)*k5+(2/55)*k6)*h;
end
Here I attached my ORIGINAL PROBLEM:

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采纳的回答

James Tursa
James Tursa 2021-11-11
The image appears to show seven equations (H1', H2', ..., H7') with boundary conditions at 0 and infinity. The RK45 scheme you are using is for initial value problems, not boundary value problems. You need to use a different method.

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