- #1
eljose
- 484
- 0
let be the integral equation:
f(x)=\lambda \int_{0}^{1}dyK(x,y)f(y)
where the Kernel is known and "lambada" is an small eigenvalue... the question is if i want to solve i propose the iterative scheme:
f_{n+1} (x)=\lambda \int_{0}^{1}dyK(x,y)f_n(y)
My question is if in this case i can propose a "Neumann series" for the resolvent Kernel R(x,y) in the form...
R= \sum_{n=0}^{\infty} \lambda ^ n K^{n}
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.
f(x)=\lambda \int_{0}^{1}dyK(x,y)f(y)
where the Kernel is known and "lambada" is an small eigenvalue... the question is if i want to solve i propose the iterative scheme:
f_{n+1} (x)=\lambda \int_{0}^{1}dyK(x,y)f_n(y)
My question is if in this case i can propose a "Neumann series" for the resolvent Kernel R(x,y) in the form...
R= \sum_{n=0}^{\infty} \lambda ^ n K^{n}
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.
