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January 1st, 2011, 09:52 AM   #1
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System of odes, Problem

Hello, i would appretiate some help on this...

My initial problem is y''=-100y+sin(y), y(0)=0, y'(0)=1, tspan[0,20*pi]
and i wanna solve it with Runge-kutta 4 stage,for Xj, j = [0 20], then i ll use this 20 initial values for solving the equations with another method of order 15. I m pasting my code, and i hope someone can figure whats wrong....

xronos = [0 20*pi];
h = (xronos(2)-xronos(1))/n;
t_dian=(xronos(1):h:xronos(2))';


x(1) = 0;
y(1) = 0;
vx(1) = 1;
vy(1) = 0;
z(1,:)=[x(1) y(1) vx(1) vy(1)];

for j=1:20
initial_buffer(1,:)=z;
akrivis_third = feval('methodosbuffer',initial_buffer(j,:),h,t_dia n,j);
initial_buffer(j+1,:)=akrivis_third(j,:);
end


%methodosbuffer


function buffer = methodosbuffer(z,h,t_dian,j)
b=1;
vima=h/6;
test(1,:)=z;
for a=t_dian(j):vima:t_dian(j+1)
testbtonos(b,:)=feval('nonlinear1',test(b,:),t_dia n(j+1));
s1 = testbtonos(b,1:2);
s2 = testbtonos(b,1:2) + ((vima/2)* s1);
s3 = testbtonos(b,1:2) + ((vima/2)* s2);
s4 = testbtonos(b,1:2) + vima * s3;
test(b+1,1:2) = test(b,1:2) + (vima/6)* (s1 + 2*s2 + 2*s3 + s4);
testbtonos(b,:)=feval('nonlinear1',test(b,:),t_dia n(j+1));
s5 = testbtonos(b,3:4);
s6 = testbtonos(b,3:4) + ((vima/2)* s1);
s7 = testbtonos(b,3:4) + ((vima/2)* s2);
s8 = testbtonos(b,3:4) + vima * s3;
test2(b+1,1:2) = test(b,1:2) + (vima/6)* (s5 + 2*s6 + 2*s7 + s8);
buffer(j,:) =test(b+1,:);
b=b+1;
end


%nonlinear1

function ztonos =nonlinear1(z,t)
y=z(1);
yp=z(3);
ydp = -100*y + sin(y);
ztonos= [yp 0 ydp 0];

Tnx, in advance.

Last edited by greg1313; October 12th, 2014 at 06:17 PM.
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