Representing and approximating third order differential equations
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I am trying to approximate a differential equation in terms of two vectors, x any y and also return a value of a solution. My differential equation is hard to represent though:
d3y/dx3 + dy/dx - xy + d2y/dx2 = 2 xE[1, 5]
initial conditions y(0), dy/dx(0) and d2y/dx2(0) have been given.
Any suggestions?
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回答 (1 件)
Francisco Angel
2014 年 4 月 3 日
編集済み: Francisco Angel
2014 年 4 月 3 日
Transform the problem in a system of first order differential equations:
dy1 / dx = y2 dy2 / dx = y3 dy3 / dx = 2-y3-x*y1-y2
with initial conditions y1(0) y2(0) and y3(0) then solve it using ode45 for example:
if true
% code
[t,Y]=ode45(@system,[1 5],[y1(0) y2(0) y3(0)]);
function dy=system(X,Y)
dy(1)=Y(2);
dy(2)=Y(3);
dy(3)=2-Y(3)-X*Y(1)-Y(2);
dy=dy';
end
end
In doubt check formatting issues tipyng help ode45 in command line.
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