Numerical solution for stochastic heat equation with Neumann boundary conditions

IF 1.1 4区工程技术 Q4 THERMODYNAMICS

Thermal Science Pub Date : 2023-01-01 DOI:10.2298/tsci23s1057r

S. Raja Balachandar, D. Uma, H. Jafari, S. Venkatesh

引用次数: 0

Abstract

In this article, we propose a new technique based on 2-D shifted Legendre poly?nomials through the operational matrix integration method to find the numeri?cal solution of the stochastic heat equation with Neumann boundary conditions. For the proposed technique, the convergence criteria and the error estima?tion are also discussed in detail. This new technique is tested with two exam?ples, and it is observed that this method is very easy to handle such problems as the initial and boundary conditions are taken care of automatically. Also, the time complexity of the proposed approach is discussed and it is proved to be O[k(N + 1)4] where N denotes the degree of the approximate function and k is the number of simulations. This method is very convenient and efficient for solving other partial differential equations.

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具有Neumann边界条件的随机热方程的数值解

在本文中，我们提出了一种基于二维移位勒让德多边形的新技术。通过运算矩阵积分法求多项式的数值?具有诺伊曼边界条件的随机热方程的计算解。对于所提出的技术，收敛准则和误差估计?并对其进行了详细的讨论。这项新技术通过两次考试来检验。结果表明，该方法可以很容易地处理自动处理初始条件和边界条件的问题。此外，本文还讨论了该方法的时间复杂度，并证明了该方法的时间复杂度为O[k(N + 1)4]，其中N表示近似函数的程度，k表示模拟次数。这种方法对于求解其他偏微分方程非常方便和有效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Thermal Science 工程技术-热力学

CiteScore

2.70

自引率

29.40%

发文量

399

审稿时长

5 months

期刊介绍： The main aims of Thermal Science to publish papers giving results of the fundamental and applied research in different, but closely connected fields: fluid mechanics (mainly turbulent flows), heat transfer, mass transfer, combustion and chemical processes in single, and specifically in multi-phase and multi-component flows in high-temperature chemically reacting flows processes present in thermal engineering, energy generating or consuming equipment, process and chemical engineering equipment and devices, ecological engineering, The important characteristic of the journal is the orientation to the fundamental results of the investigations of different physical and chemical processes, always jointly present in real conditions, and their mutual influence. To publish papers written by experts from different fields: mechanical engineering, chemical engineering, fluid dynamics, thermodynamics and related fields. To inform international scientific community about the recent, and most prominent fundamental results achieved in the South-East European region, and particularly in Serbia, and - vice versa - to inform the scientific community from South-East European Region about recent fundamental and applied scientific achievements in developed countries, serving as a basis for technology development. To achieve international standards of the published papers, by the engagement of experts from different countries in the International Advisory board.