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?
What is the difference between resolvent kernel and iterative kernel of an integral equation?
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integral-transforms
integral-equations
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0Please proof-read your question once before posting it. Your post had a slew of spelling mistakes [that could be easily avoided]. – 2011-11-16
1 Answers
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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. In general, we have $K_n(x,t)=\int\limits_t^x K(x,z)⋅K_{n-1}(z,t)dz$.
Whereas Resolvent Kernel $R$ is defined as $R(x,t)=\sum_i\lambda^{i-1} K_i(x,t)$.