Advanced Mathematical Models & Applications

ISSN Online: 2519-4445

Advanced Mathematical Models & Applications is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues.

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Cubic Generalized B-Spline Quasi Interpolation Scheme for Solving Nonlinear Burgers' Equation

Published: 02-08-2026

https://doi.org/10.62476/amma112327

Abstract

In the present work, a new scheme based on a cubic generalized quasi-interpolator (CGQI) has been developed to evaluate new numerical results of the nonlinear Burgers equation. In a first step, the Burgers equation is remodeled into a set of linear systems, in which an accurate fourth-order approximation of the unknown functions is obtained via CGQI. The accuracy, efficiency, and effectiveness of the developed CGQI technique are demonstrated on four different examples of nonlinear Burgers equations by calculating the error norms: L₂ and L_∞ errors. The proposed CGQI scheme is also tested for the nonlinear Burger equation with very small kinematic viscosities. Numerical results show that the developed CGQI performs better than some recently developed techniques.