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

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.