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Random heat equation: Solutions by the stochastic adaptive interpolation method

By N. Bellomo, L.M. de Socio and R. Monaco

Abstract

AbstractThe one-dimensional nonlinear heat equation is considered with stochastic coefficients and initial/boundary values in a finite strip and in the half-space. Approximated solutions are obtained by the stochastic adaptive interpolation method which corresponds first to transforming the original partial differential equation into a system of ordinary differential equations via a generalization to the stochastic case of the Bellman's differential quadrature method. The system of ordinary differential equations is then solved by a continuous approximation following by Adomian's decomposition method, and the solutions are compared with those obtained by more standard numerical techniques

Publisher: Published by Elsevier Ltd.
Year: 1988
DOI identifier: 10.1016/0898-1221(88)90011-9
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