Scholarlink

<p>In the present study, we shall be concerned with the numerical solution of a multi-term Caputo temporal fractional advection-diffusion (MTFAD) equation with the weak singularity at the initial time. The numerical methods are designed by considering three different kinds of mesh in the temporal domain of the problem, such as adaptive, graded and uniform. The temporal fractional derivative (TFD) is approximated by using the L1 technique on nonuniform grid or uniform grid. The adaptive mesh is generated via equidistribution of a positive monitor function. A fourth-order compact finite difference (CFD) method is designed to approximate the space derivatives in the resultant semi-discretized problems. The graded mesh scheme is proven to be unconditionally stable and convergence analysis of the numerical scheme is investigated. Two numerical examples with nonsmooth and smooth exact solutions are solved to demonstrate the accuracy of the method. The numerical results obtained on adaptive, graded and uniform meshes are compared against each other. The elapsed computational times for the suggested numerical algorithms are provided.</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

Two efficient non-uniform mesh numerical techniques for a multi-term time-fractional advection-diffusion equation: Moving mesh method

  • 期刊论文

  • 发表日期：

    2025年3月20日

查看全文
  • Pradip Roul,
  • S. Sundar

摘要

In the present study, we shall be concerned with the numerical solution of a multi-term Caputo temporal fractional advection-diffusion (MTFAD) equation with the weak singularity at the initial time. The numerical methods are designed by considering three different kinds of mesh in the temporal domain of the problem, such as adaptive, graded and uniform. The temporal fractional derivative (TFD) is approximated by using the L1 technique on nonuniform grid or uniform grid. The adaptive mesh is generated via equidistribution of a positive monitor function. A fourth-order compact finite difference (CFD) method is designed to approximate the space derivatives in the resultant semi-discretized problems. The graded mesh scheme is proven to be unconditionally stable and convergence analysis of the numerical scheme is investigated. Two numerical examples with nonsmooth and smooth exact solutions are solved to demonstrate the accuracy of the method. The numerical results obtained on adaptive, graded and uniform meshes are compared against each other. The elapsed computational times for the suggested numerical algorithms are provided.