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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

CW answer to remove it from unanswered queue:

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 $R(x,t)=\sum_i\lambda^i K_i(x,t)$.

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