Abstract
It is suggested to transform a class of nonlinear differential equations with a holomorphic type of nonlinearity into linear integrodifferential equations. The method is presented in detail for first-order ordinary differential equations. The transformed equation is studied and is found to have a unique solution with an analytical representation. In a numerical test calculation rapid convergence of an approximate solution of the linearized equation towards the reference solution is found. The method can be applied to higher-order ordinary and partial differential equations. The transformation can be generalized also to operator-valued differential equations.
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