N-Dimensional quartic B-spline collocation method to solve different types of n-dimensional partial differential equations

Raslan, K. R.; Ali, Khalid K.; Shaalan, M.A.

doi:10.1016/j.joes.2022.06.034

Cited by 1 publication

(2 citation statements)

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“…By making the substitution from equations ( 6)-( 7) into equations (15) with (18), we are able to obtain the numerical results that are presented in the following table . Table 3 presents the results that were obtained using the two-dimensional spherical B-spline method for the value of 50 × 50. When it comes to the results, we may safely assume that they meet our expectations.…”

Section: Te Second Test Problemmentioning

confidence: 99%

“…Tey discussed extended cubic Bsplines [11], n-dimensional quadratic B-splines [12], as well as three-and four-dimensional cubic and trigonometric B-spline collocation methods [13,14]. Te n-dimensional quartic and quintic B-spline collocation methods were investigated in separate studies [15,16]. Boundary value problems have been studied using B-spline methods in many papers [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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

Ali,

Raslan,

Mohamed

2024

Journal of Mathematics

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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.

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Section: Te Second Test Problemmentioning

confidence: 99%