Efficient stochastic collocation techniques for transient heat equations with uncertain inputs

Abstract

This study develops an efficient numerical framework for transient heat equations with uncertain diffusion and Robin boundary parameters. The approach combines a stochastic collocation method to handle parametric uncertainty with a finite difference scheme for time integration. Convergence and stability properties of the method are established under suitable assumptions on the random inputs. Numerical results confirm the accuracy and computational efficiency of the proposed approach for uncertainty quantification in transient heat transfer problems.