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<p>A brain tumor is a life-threatening disease caused by the atypical and uncontrolled growth of cells that can invade other parts of the body. Due to its rapid growth, the dynamics of brain tumors are quite complex, making any prediction challenging. Therefore, an extended mathematical model is simulated under favorable conditions. To characterize the density of brain tumors, a reliable and effective numerical technique based on a hybrid b-spline shape function with collocation strategy has been implemented. Additionally, the Von-Neumann stability analysis and convergence analysis presented in this study demonstrate the effectiveness and durability of the scheme. The results of the technique are illustrated via 2D and 3D visualization, the approximate solution, and finally, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> <i>RMS</i> and Relative error norms have been calculated. The novelty of the current work is the method's ability to handle large-scale problems and produce highly accurate outcomes.</p>

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Numerical characterization of brain tumor density using a hybrid B-spline collocation approach

  • 期刊论文

  • 发表日期：

    2025年11月14日

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  • Neelam Rana,
  • Neeraj Dhiman,
  • Robin Singh,
  • Waleed Adel

摘要

A brain tumor is a life-threatening disease caused by the atypical and uncontrolled growth of cells that can invade other parts of the body. Due to its rapid growth, the dynamics of brain tumors are quite complex, making any prediction challenging. Therefore, an extended mathematical model is simulated under favorable conditions. To characterize the density of brain tumors, a reliable and effective numerical technique based on a hybrid b-spline shape function with collocation strategy has been implemented. Additionally, the Von-Neumann stability analysis and convergence analysis presented in this study demonstrate the effectiveness and durability of the scheme. The results of the technique are illustrated via 2D and 3D visualization, the approximate solution, and finally, the \(L_{2}\) L 2 , \(L_{\infty }\) L ∞ RMS and Relative error norms have been calculated. The novelty of the current work is the method's ability to handle large-scale problems and produce highly accurate outcomes.