Abstract
A new approximation technique is suggested for coagulation equations which is remarkably accurate. This technique leads to a new form for the discrete coagulation equation. This method has been applied to several different initial distributions for both physical and mathematical kernels. Furthermore, our method indicates that taking the first moment as a criterion for accuracy of the integration method is misleading and yields erroneous conclusions. The approximate polynomial solution to the coagulation equations for an arbitrary kernel has also been investigated. It is found that the polynomial solution is very accurate and easy to apply for the case of a constant kernel but, for a variable kernel, it may be applied only to cases where the fluctuation of the kernel from its average value is very small. The appearance of the second peak for the initial gamma distribution is observed for all kernels applied here.
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