Work

High-Order Approximations for a Pseudoparabolic Equation of Turbulent Mass-Transfer Diffusion

Year: 2025

Type: article

Abstract: Numerical solutions of turbulent mass-transfer diffusion present challenges due to the nonlinearity of the elliptic–parabolic degeneracy of the mathematical models. Our main result in this paper concerns the development and implementation of an efficient high-order numerical method that is fourth-order accurate in space and second-order accurate in time for computing both the solution and its gradient for a Barenblatt-type equation. First, we reduce the original Neumann boundary value problem to a Dirichlet problem for the equation of the solution gradient. This problem is then solved by a compact fourth-order spatial approximation. To implement the numerical discretization, we employ Newton’s iterative method. Then, we compute the original solution while preserving the order of convergence. Numerical test results confirm the efficiency and accuracy of the proposed numerical scheme.

Source: Axioms

DOI: 10.3390/axioms14040319

Authors: Miglena N. Koleva, Lubin G. Vulkov

Institution: Angel Kanchev University of Ruse

Language: English

Topic: Differential Equations and Numerical Methods

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: European Commission