Abstract

The need for remeshing when computing flow problems in domains suffering large deformations has motivated the implementation of a tool that allows the proper transmission of information between finite element meshes. Because the Lagrangian projection of results from one mesh to another is a dissipative method, a new conservative interpolation method has been developed. A series of constraints, such as the conservation of mass or energy, are applied to the interpolated arrays through Lagrange multipliers in an error minimization problem, so that the resulting array satisfies these physical properties while staying as close as possible to the original interpolated values in the L2 norm. Unlike other conservative interpolation methods that require a considerable effort in mesh generation and modification, the proposed formulation is mesh independent and is only based on the physical properties of the field being interpolated. Moreover, the performed corrections are neither coupled with the main calculation nor with the interpolation itself, for which reason the computational cost is very low.

Abstract

Abstract

This article investigates the problem of approximating the generalized Erdélyi-Kober fractional operator (often referred to as the Lowndes operator) using cubic splines. A method based on cubic spline interpolation is proposed for approximating the operator on a non-uniform grid. The convergence rate of the proposed method is proven, and its stability is analyzed. Error bounds are established for functions in the class C4[0; b], providing a mathematical justification for the accuracy of the approximation. The efficiency of the method is validated through practical examples using test functions such as f (x)= x4.7and f (x)= cos x, with results presented in graphical and numerical forms. This approach ensures high accuracy and flexibility in computing fractional integrals, which is of significant importance for solving fractional models used in physics, engineering, and other sciences. The article also provides an overview of the role of the generalized Erdélyi-Kober operator in modern fractional calculus and its applications.OPEN ACCESS Received: 06/06/2025 Accepted: 08/09/2025 Published: 27/10/2025

Abstract

This article investigates the problem of approximating the generalized Erdélyi-Kober fractional operator (often referred to as the Lowndes operator) using cubic splines. A method based on cubic spline interpolation is proposed for approximating the operator on a non-uniform grid. The convergence rate of the proposed method is proven, and its stability is analyzed. Error bounds are established for functions in the class C4[0; b], providing a mathematical justification for the accuracy of the approximation. The efficiency of the method is validated through practical examples using test functions such as f (x)= x4.7and f (x)= cos x, with results presented in graphical and numerical forms. This approach ensures high accuracy and flexibility in computing fractional integrals, which is of significant importance for solving fractional models used in physics, engineering, and other sciences. The article also provides an overview of the role of the generalized Erdélyi-Kober operator in modern fractional calculus and its applications.OPEN ACCESS Received: 06/06/2025 Accepted: 08/09/2025 Published: 27/10/2025

Abstract

This article investigates the problem of approximating the generalized Erdélyi-Kober fractional operator (often referred to as the Lowndes operator) using cubic splines. A method based on cubic spline interpolation is proposed for approximating the operator on a non-uniform grid. The convergence rate of the proposed method is proven, and its stability is analyzed. Error bounds are established for functions in the class C4[0; b], providing a mathematical justification for the accuracy of the approximation. The efficiency of the method is validated through practical examples using test functions such as f (x)= x4.7and f (x)= cos x, with results presented in graphical and numerical forms. This approach ensures high accuracy and flexibility in computing fractional integrals, which is of significant importance for solving fractional models used in physics, engineering, and other sciences. The article also provides an overview of the role of the generalized Erdélyi-Kober operator in modern fractional calculus and its applications.OPEN ACCESS Received: 06/06/2025 Accepted: 08/09/2025 Published: 27/10/2025

Abstract