This paper presents an efficient computational approach based on 9th order(nonic) B-spline basis functions for the numerical solution of the seventh-order nonlinear Korteweg–de Vries (KdV) equation. The novel method takes advantage of the greater smoothness and accuracy of derivatives of nonic B-splines and is thus able to achieve accurate spatial approximations, most appropriately suited to accommodate the intricate dispersive nature inherent in higher-order wave equations. The nonlinear terms are based on Taylor series expansions, and time discretization is carried out through an implicit Crank–Nicolson integration scheme. The method proposed is validated through analysis on several classic seventh-order integrable KdV equations, viz., the Kaup–Kuperschmidt, Lax, and Sawada–Kotera equations. The numerical results exhibit very good agreement with analytical expectations and demonstrate uniformly lower maximum error norms than existing methods. These findings confirm the validity and efficiency of the nonic B-spline collocation scheme for simulating strongly dispersive wave propagation modeled by complex nonlinear partial differential equations.
In this work, we revisit the notion of γ -contractions on fuzzy metric spaces and prove some fixed point results by improving the definition of γ -contractions. The obtained results extend and generalize the fixed point results for γ -contractions and several other results in fuzzy metric spaces. Some examples are provided to justify our claims and illustrate the results. As a consequence, we derive fuzzy and local versions of fixed point results of Banach [2] and Reich [32], and utilize them in solving the existence problem arising in fractional-order Chua’s circuits.
In this paper, we have generalized Bor's Theorem [1] for absolute summability method.
This study presents the heat transfer analysis of magnetohydrodynamic trihybrid nanofluid flow over a stretching Riga surface configuration and the Cattaneo–Christov non-Fourier heat flux model. The electrically conducting Al_2O_3 –Cu– TiO_2 /water trihybrid nanofluid flows over a convectively heated stretching Riga plate, where a wall-parallel Lorentz force alters the boundary layer structure. Finite-speed thermal propagation is captured through the inclusion of thermal relaxation effects. By employing similarity transformations, the governing equations are reduced to a coupled system of nonlinear ordinary differential equations and solved numerically using MATLAB’s bvp4c solver. The effects of the electromagnetic force, magnetic interaction, nanoparticle volume fractions and thermal relaxation parameters on velocity and temperature distributions are analyzed. The results provide new insights into efficient thermal management using trihybrid nanofluids over advanced electromagnetic surfaces.
