2
votes
2answers
54 views

Uniform convergence of matrix integral sequence

I was given recursively defined: $M_k=I+\int_{t_0}^tA(s)M_{k-1}(s)~ds$ and $M_0=I$ and that $A(t)$ is a matrix with entries that are continuous functions on $t_0\leq t\leq t_1$. By induction we can ...
7
votes
1answer
211 views

Fredholm Equations

I have the following problem to solve $$\phi (x)=\lambda \int_{o}^{\pi }\cos(2x+y)\phi (y) dy+ \sin x$$ following the instructions from the following link early to conclude that: $$\phi (x)=\lambda ...
1
vote
2answers
431 views

Find the eigenvalues and eigenvectors of an integral operator

I need to find the eigenvalues e eigenvectors of this integral. $$\int_{0}^{1} K(x,y)\phi (y)dy,$$ where $K(x,y)=x(1-y),\; 0 \le x\le y \le 1$ and $K(x,y)=y(1-x),$ $0\le y\le x \le 1$ I ...
3
votes
2answers
166 views

Solve integral equation of second kind using Fredholm method

I need to solve this integral equation $$\phi (x)=(x^2-x^4)+ \lambda \int_{-1}^{1}(x^4+5x^3y)\phi (y)dy$$ Using the Fredholm theory of the intergalactic equations of second kind. I really don't ...
2
votes
1answer
95 views

Matrix inversion of an analytical function

Following problem: I have a function $f(x_1,x_2)$ and Im looking for the inverse $finv(x_1,x_2)$ of the function which is defined through: $\int f(x_1,y)\cdot finv(y,x_2) d y =\delta(x_1,x_2) $ ...
0
votes
1answer
189 views

Linear versus non-linear integral equations

I'm having trouble solving an integral equation. It appears to me to be a homogeneous Fredholm equation of the second kind. However, I'm being told that this can't be a Fredholm equation, because it ...