An hybrid deterministic-stochastic iterative procedure to solve the heat equation
Fouad Maouche
TL;DR
This paper introduces a hybrid deterministic-stochastic iterative method combining Crank-Nicolson discretization and Robbins-Monro stochastic approximation to solve the 1-D heat equation, with proven convergence properties.
Contribution
It presents a novel hybrid approach that integrates deterministic discretization with stochastic approximation for solving PDEs, along with convergence analysis.
Findings
Proven almost complete convergence of the method
Established the rate of convergence
Demonstrated effectiveness for the 1-D heat equation
Abstract
Our goal in this paper is to solve the 1-D heat equation by an hybrid deterministic-stochastic iterative procedure . The deterministic side consists in discretizing the equation by the Crank-Nicolson method and the stochastic side consists of applying Robbins Monro procedure to solve the resulting matrix system. The almost complete convergence and the rate of convergence of our procedure are established.
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Taxonomy
TopicsMatrix Theory and Algorithms · Statistical and numerical algorithms · Advanced Optimization Algorithms Research