Abstract
A method is given for solving certain infinite-order differential equations whose characteristic function is an entire function of order less than 1. The infinite-order operator is expressed as an infinite product of first-order operators and is then inverted by a sequence of integral operators. The method is a natural generalization of a finite-order method and can be computed numerically. The method is shown to converge and an error estimate is given. Applications to solutions of some heat equation problems are indicated.
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