Recent content by akanksha331

I am a little unsure if I have the correct approach but here goes U(x,0) = X(x)T(0) = sin(pi*x/L) (the initial condition) Let a=pi/L then X(x) = sin(ax)/T(0), Here, X(0)T(t) = X(L)T(0) = 0 (the boundary conditions) Substituting this back in the original equation gives: d/dt[T(t)]*sin(ax) +...

I am sure I can solve the problem . I just want one hint to start the problem.

Let a,b,c be three 3x1 vectors. Let A be a 3x3 upper triangular matrix which ensures that the 3x1 vectors d,e and f obtained using [d e f]=A[a b c] are orthogonal. a)Express the elements of A in terms of vectors a,b and c. b)what is the condition on a,b and c which allows us to find an...

Solve BVP by separating variables and using eigenfunction expansion method PDE:Ut-Uxx=e-2tsin(pi x/L) U=U(x,t),x(0,L) BC1:U(0,t)=0 BC2:U(L,t)=0 IC:U(x,0)=sin(pi x/L) U(x,t)=X(x)T(t),X''=(lambda) X ,lambda is the separation of parameter. I have calculated the basis functions...

A=a.a', where a is an N by 1 vector,a'a=5,and T is transpose. a)Give the largest eigenvalue of A. b)what is the corresponding eigenvector? Please help me to solve the problem.