Scholarlink

<p>This work aims to propose an efficient dimension-reducing numerical technique for solving a two-dimensional (2D) nonlinear space-fractional diffusion equation (SFDE). The model problem is initially linearized to enable a more efficient formulation of the numerical scheme. The motive of this work is to establish a splitting technique to reduce the computation cost. This is achieved by partitioning the given 2D model problem into a set of two distinct one-dimensional (1D) problems along both the <i>x</i> and <i>y</i> directions and the error estimate of the proposed scheme is studied. The space-fractional term is approximated utilizing the well-known <i>L</i>1-method over a uniform mesh and thereafter the discrete maximum principle is studied for the discretized scheme. To support the convergence analysis, a suitable discrete barrier function is developed and used. The validity of the theoretical estimations and the proposed numerical technique is demonstrated through numerical experiments.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An Effective Dimension-Reducing Technique for Two-Dimensional Nonlinear Space-Fractional Diffusion Equation

  • 期刊论文

  • 发表日期：

    2026年1月22日

查看全文
  • Aniruddha Seal,
  • Srinivasan Natesan

摘要

This work aims to propose an efficient dimension-reducing numerical technique for solving a two-dimensional (2D) nonlinear space-fractional diffusion equation (SFDE). The model problem is initially linearized to enable a more efficient formulation of the numerical scheme. The motive of this work is to establish a splitting technique to reduce the computation cost. This is achieved by partitioning the given 2D model problem into a set of two distinct one-dimensional (1D) problems along both the x and y directions and the error estimate of the proposed scheme is studied. The space-fractional term is approximated utilizing the well-known L1-method over a uniform mesh and thereafter the discrete maximum principle is studied for the discretized scheme. To support the convergence analysis, a suitable discrete barrier function is developed and used. The validity of the theoretical estimations and the proposed numerical technique is demonstrated through numerical experiments.