# What is the difference between resolvent kernel and iterative kernel of an integral equation?

As we have different methods to find resolvent kernel, which is more suitable among all those methods? And what is the difference between resolvent and iterative kernels?

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Suppose $K(x,t)=K_{1}(x,t)$ is your 1st kernel then $K_{2}(x,t)=\int\limits_{t}^{x} k(x,z) \cdot K_{1}(z,t) \ dz$. This $K_{2}(x,t)$ is called as the iterated kernel. Whereas Resolvent Kernel $R$ is defined as $R(x,t) = \sum_{i} K_{i}(x,t)$. – user9413 Nov 16 '11 at 15:40
Please proof-read your question once before posting it. Your post had a slew of spelling mistakes [that could be easily avoided]. – Srivatsan Nov 16 '11 at 17:21

Suppose $K(x,t)=K_1(x,t)$ is your $1^{st}$ kernel then $K_2(x,t)=\int\limits_t^x K(x,z)⋅K_1(z,t)dz$. This $K_2(x,t)$ is called as the iterated kernel.
Whereas Resolvent Kernel $R$ is defined as $R(x,t)=\sum_iK_i(x,t)$.