Central limit theorem for a fractional stochastic heat equation with spatially correlated noise

Li, Yumeng

doi:10.1186/s13662-020-02562-8

Cited by 1 publication

(1 citation statement)

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“…In this work, the heat conduction equation is simulated to obtain the temperature patterns in a thin bar [21][22][23]. The analysis of non-stationary heat transfer is of practical interest, not only because of the importance that cooling and heating processes have in a large number of industrial applications but also because of their similarity with several other equations of physics-mathematics that present the same difficulties to be solved numerically.…”

Section: Introductionmentioning

confidence: 99%

Convergency and Stability of Explicit and Implicit Schemes in the Simulation of the Heat Equation

Carreño

Rosales-Romero

2021

Applied Sciences

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Some strategies for solving differential equations based on the finite difference method are presented: forward time centered space (FTSC), backward time centered space (BTSC), and the Crank-Nicolson scheme (CN). These are developed and applied to a simple problem involving the one-dimensional (1D) (one spatial and one temporal dimension) heat equation in a thin bar. The numerical implementation in this work can be used as a preamble to introduce a method of solving the heat equation that can be implemented in problems in the area of finances. The results of implementing the software on very fine meshes (unidimensional), and with relatively small-time steps, are shown. Through mesh refinement, it was possible to obtain a better temperature distribution in the thin bar between a range of points. The heat equation was solved numerically by testing both implicit (CN) and explicit (FTSC and BTSC) methods. The examples show that the implemented schemes conform to theoretical predictions and that truncation errors depend on mesh, spacing, and time step.

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Section: Introductionmentioning

confidence: 99%