- #1
eljose
- 492
- 0
let be the integral equation:
[tex] f(x)=\lambda \int_{0}^{1}dyK(x,y)f(y) [/tex]
where the Kernel is known and "lambada" is an small eigenvalue... the question is if i want to solve i propose the iterative scheme:
[tex] f_{n+1} (x)=\lambda \int_{0}^{1}dyK(x,y)f_n(y) [/tex]
My question is if in this case i can propose a "Neumann series" for the resolvent Kernel R(x,y) in the form...
[tex] R= \sum_{n=0}^{\infty} \lambda ^ n K^{n} [/tex]
for K^n the n-th iterated kernel since the equation is HOmogeneus (all the functions involved except the Kernel are unknown) or if we have enough with the iteration procedure to solve the equation..thanks.
[tex] f(x)=\lambda \int_{0}^{1}dyK(x,y)f(y) [/tex]
where the Kernel is known and "lambada" is an small eigenvalue... the question is if i want to solve i propose the iterative scheme:
[tex] f_{n+1} (x)=\lambda \int_{0}^{1}dyK(x,y)f_n(y) [/tex]
My question is if in this case i can propose a "Neumann series" for the resolvent Kernel R(x,y) in the form...
[tex] R= \sum_{n=0}^{\infty} \lambda ^ n K^{n} [/tex]
for K^n the n-th iterated kernel since the equation is HOmogeneus (all the functions involved except the Kernel are unknown) or if we have enough with the iteration procedure to solve the equation..thanks.