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Abstract <p>On the basis of hyperbolic heat conduction equation, three-layer compact difference schemes of orders 4 + 2, 4 + 4 and a Saul’ev scheme of order 6 + 3 are constructed on minimal three-point stencils in space. The close relationship between the explicit Chetverushkin scheme and the three-layer asymptotically stable Samarskii scheme is shown. It is also proposed to combine the classical models of filtration and heat conduction into a single mathematical model based on the definition of a generalized solution according to Godunov. The algorithms of order 4 + 2 obtained in this way are generalized to quasi–linear parabolic equations with arbitrary nonlinearity. Numerical calculations of a number of test problems are given, illustrating the efficiency of compact schemes.</p>

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Three-Layer Compact Difference Scheme for a Hyperbolic Heat Conduction Equation

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • P. P. Matus,
  • V. T. K. Tuyen,
  • B. D. Utebaev

摘要

Abstract

On the basis of hyperbolic heat conduction equation, three-layer compact difference schemes of orders 4 + 2, 4 + 4 and a Saul’ev scheme of order 6 + 3 are constructed on minimal three-point stencils in space. The close relationship between the explicit Chetverushkin scheme and the three-layer asymptotically stable Samarskii scheme is shown. It is also proposed to combine the classical models of filtration and heat conduction into a single mathematical model based on the definition of a generalized solution according to Godunov. The algorithms of order 4 + 2 obtained in this way are generalized to quasi–linear parabolic equations with arbitrary nonlinearity. Numerical calculations of a number of test problems are given, illustrating the efficiency of compact schemes.