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A Novel Generalized n-Dimensions Sixtic B-Spline Function to Solving n-Dimensions Mathematical Models

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  • Khalid K. Ali
  • K. R. Raslan
  • Mohamed S. Mohamed
  • Dengfeng Lü

Abstract

In this study, we present a novel framework for the sixtic B-spline collocation approach in n-dimensions. Building upon previous research that focused on developing B-spline functions in n-dimensions to solve mathematical models, this work represents an extension of those efforts. We provide formulations of the sixtic B-spline collocation algorithm in one-dimensional, two-dimensional, and three-dimensional settings. These structures play a crucial role in solving mathematical models across diverse fields of study. To showcase the efficacy and accuracy of the proposed method, we employ a range of test problems in two and three dimensions. These examples serve as demonstrations of the effectiveness and precision of the suggested approach.

Suggested Citation

  • Khalid K. Ali & K. R. Raslan & Mohamed S. Mohamed & Dengfeng Lü, 2024. "A Novel Generalized n-Dimensions Sixtic B-Spline Function to Solving n-Dimensions Mathematical Models," Journal of Mathematics, Hindawi, vol. 2024, pages 1-30, April.
    • Handle: RePEc:hin:jjmath:3886554
    DOI: 10.1155/2024/3886554
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