Characterizing magnetohydrodynamical and induced magnetic effects inside a square channel using an inventive combination of spectral and one-step techniques

Physics of Fluids, Journal Year: 2025, Volume and Issue: 37(2)

Published: Feb. 1, 2025

A difficult matter for researchers is to develop numerical methods analyze the behavior of nonlinear dynamical systems that arise in mathematical physics due their nonlinearity and multi-dimensional nature. In this affection, a novel effective coupling spectral one-step approaches suggested used inspect robust solutions problems. This proposed method grounded on sixth-order Runge–Kutta (RK) shifted Vieta–Fibonacci (sVF) polynomial-based approach. First, use technique temporal approximation, then utilize sVF polynomials estimate spatial variables. The new operational matrices are calculate derivative terms models. Related theorems presented paper provide validation technique. semi-spectral techniques transform investigated models into set linear algebraic equations, making them simpler solve. We conduct theoretical research stability, convergence, error-bound analysis support computational algorithm's formulation. Several models, including Hartmann numbers ranging from 0 106, taken consideration demonstrate precision efficacy thorough comparison illustrates recommended approach's validity, correctness, dependability. construction direction exponential order around 3.5545e0.1515M determined be exceptional handling problems examining exact solutions.

Language: Английский

Novel connection of spectral scheme and one-step of s-order approaches for MHD flows enclosed a duct

Computers & Mathematics with Applications, Journal Year: 2025, Volume and Issue: 184, P. 185 - 220

Published: March 4, 2025

Language: Английский