I need help solving this second order differential equation?
조회 수: 1 (최근 30일)
이전 댓글 표시
I was given a second order function that models longitudinal displacements in a longitudinally loaded elastic bar.
a(x)*u''(x) + a'(x)*u'(x)=f(x), 0 <= x <=1
I know that the left end is at x=0 and the right end is at x=1. So that means:
u(0)=u(1)=0 (does not bend at the ends)
I know a(x) represents both the elastic properties and the cross-sectional area of the bar and u(x) is the displacement at point x.
for the first part I am told that a(x)=1+x and f(x)= 5*sin(2*pi*x)^2 (this is the case where the force is applied symetrically and is strongest at x=.25 and x=.75)
I need to use dsolve to solve for the problem and plot the result on the interval [0,1]
This is what I tried to do:
ode1= 'D2y*(1+x)+ Dy= 5*sin(2*pi*x)^2';
sol=dsolve(ode1,'y(0)=0','y(1)=0');
ezplot(sol)
Howver the graph I got from this just does not look right. Can someone please help me out?
댓글 수: 11
Walter Roberson
2011년 8월 7일
My mistake earlier: Ei is the Exponential Integral, not the Elliptic Integral. The hypergeometric conversion I showed is still valid, though.
I do see any immediate reason why you would be getting the str2num errors, but I can make the suggestion that you optimize using
t = mfun('Ei', pi*i*[-4, 4, -8, 8, -4*(x+1), 4*(x+1)]);
and then replace the individual mfun calls with t(1), t(2), t(5, t(6), t(1), t(2), t(3), and t(4) respectively.
답변 (1개)
Neels
2011년 8월 7일
My suggestion would be to rearrange the equation as
u''(x) =f(x)/a(x)- u'(x)/a(x)
z = f(x)/a(x)-y/a(x) , where y is first derivative of u(x) and z is first derivative of y. Then solve it using ode45, giving the initial values. I think matlab computes faster using first order derivatives
참고 항목
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!