Scholarlink

<p>We propose a new numerical method for solving the nonlinear collisional breakage equation, based on a birth modification strategy that employs volume average in each cell to allocate newly born particles across three adjacent cells. The scheme shows enhanced accuracy and efficiency compared to existing numerical schemes over different possible choices of grids: uniform, nonuniform, locally uniform, random and oscillatory grids. A detailed convergence and error analysis demonstrates first-order accuracy over all these grids. Moreover, certain examples exhibit an increase in convergence order over uniform, nonuniform and locally uniform grids, while maintaining first-order accuracy over random and oscillatory grids. Most importantly, this technique ensures consistency over random grids, thereby improving model reliability. The method is further extended to a bivariate model on rectangular grids. Additionally, numerical results are provided to validate our proposed scheme in both one and two dimensions along with cases identifying the instance of solution blow-up.</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

Convergence rate and error analysis of a cell average technique for collisional breakage equation with bivariate modeling

  • 期刊论文

  • 发表日期：

    2026年1月7日

查看全文
  • Prakrati Kushwah,
  • Anupama Ghorai,
  • Jitraj Saha

摘要

We propose a new numerical method for solving the nonlinear collisional breakage equation, based on a birth modification strategy that employs volume average in each cell to allocate newly born particles across three adjacent cells. The scheme shows enhanced accuracy and efficiency compared to existing numerical schemes over different possible choices of grids: uniform, nonuniform, locally uniform, random and oscillatory grids. A detailed convergence and error analysis demonstrates first-order accuracy over all these grids. Moreover, certain examples exhibit an increase in convergence order over uniform, nonuniform and locally uniform grids, while maintaining first-order accuracy over random and oscillatory grids. Most importantly, this technique ensures consistency over random grids, thereby improving model reliability. The method is further extended to a bivariate model on rectangular grids. Additionally, numerical results are provided to validate our proposed scheme in both one and two dimensions along with cases identifying the instance of solution blow-up.