📄 deycjz_hm.m
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function y = DEYCJZ_hm(f, h,a,b,y0,varvec,type)
format long;
N = (b-a)/h;
y = zeros(N+1,1);
x = a:h:b;
y(1) = y0;
y(2) = y0+h*Funval(f,varvec,[x(1) y(1)]);
y(3) = y(2)+h*Funval(f,varvec,[x(2) y(2)]);
y(4) = y(3)+h*Funval(f,varvec,[x(3) y(3)]);
if type == 1
for i=5:N+1
v1 = Funval(f,varvec,[x(i-3) y(i-3)]);
v2 = Funval(f,varvec,[x(i-2) y(i-2)]);
v3 = Funval(f,varvec,[x(i-1) y(i-1)]);
t = y(i-4) + 4*h*(2*v3 - v2 + 2*v1)/3;
ft = Funval(f,varvec,[x(i) t]);
y(i) = (9*y(i-1) -y(i-3) +3*h*(2*v3 + ft-v2))/8;
end
else
p0 = 0;
c = 0;
for i = 5:N+1
v1 = Funval(f,varvec,[x(i-3) y(i-3)]);
v2 = Funval(f,varvec,[x(i-2) y(i-2)]);
v3 = Funval(f,varvec,[x(i-1) y(i-1)]);
p = y(i-4)+4*h*(2*v3 - v2 + 2*v1)/3;
M = p - 112*(p0 - c)/121;
F = Funval(f , varvec, [x(i) ,M]);
c = (9*y(i-1) -y(i-3) +3*h*(2*v3 + F-v2))/8;
y(i) = c + 9*( p - c)/121;
p0 = p;
end
end
format short;
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