This study investigates the two-dimensional magnetohydrodynamic (MHD) slip flow of a tangent-hyperbolic (TGH) aluminum-alloy hybrid nanofluid over a stretching surface in a porous medium. The model incorporates magnetic effects, velocity and thermal slip, thermal radiation, heat generation, viscous dissipation, chemical reaction, and activation energy. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations and solved numerically in MATLAB using the bvp4c solver. The effects of key parameters on the velocity, temperature, and concentration profiles are analyzed, together with the skin-friction coefficient, N... More >

This paper proposes a modified two-point block backward differentiation formula (MBBDF) for the numerical solution of highly stiff and oscillatory ordinary differential equations. The method achieves third-order accuracy with a reduced error constant and computes two solution values simultaneously at each step. For the selected parameter value $\rho=-\dfrac{7}{8}$, stability analysis shows that the resulting scheme is A-stable, making it suitable for the numerical integration of stiff initial value problems. The method is also consistent and zero-stable, and hence convergent. Numerical experiments on benchmark stiff problems show that the relative accuracy of the considered methods depends o... More >

This study investigates the order and convergence properties of an extended two-point superclass Block Backward Differentiation Formula (BBDF) incorporating two intermediate (off-step) points for the numerical solution of stiff initial value problems (IVPs). Stiff systems frequently arise in scientific and engineering applications and require numerical methods that combine stability, accuracy, and computational efficiency. While classical Backward Differentiation Formula (BDF) methods are well known for their stability, their sequential nature limits efficiency, particularly for large-scale problems. To address these limitations, the proposed framework extends the BBDF approach by introducin... More >

Daily mean PM\(_{2.5}\) concentrations in Hyderabad routinely exceed both the 24-hour (\(60\,\mu\text{g/m}^3\)) and the annual (\(40\,\mu\text{g/m}^3\)) National Ambient Air Quality Standards, motivating the development of transparent and inexpensive descriptive models of their seasonal behaviour. To this end, we develop and calibrate a parsimonious first-order linear ordinary differential equation (ODE) that describes the daily evolution of ambient PM\(_{2.5}\) as the balance between a seasonally varying emission source \(E(t)=E_{0}+A\cos(2\pi(t-\varphi)/365)\) and a wind-driven first-order removal \(\lambda(t)=\alpha v(t)+\lambda_{0}\). The five parameters are estimated by Differential Evo... More >

The modern era is characterized by rapid advancements in technology, wherein the design and topology of interconnection networks play a pivotal role in enabling efficient communication systems. The analysis of topological and structural characteristics of interconnection networks, however, remains a challenging task. Graph theory facilitates this process by enabling analytical and efficient solutions through the use of numerical parameters known as topological descriptors. These descriptors have proven to be highly significant, with applications spanning computer science, chemistry, biology, and related domains. This paper deals with the evaluation of topological descriptors for an $n$-dimen... More >

This paper develops a dynamical systems model of an economy with recursively self-improving artificial intelligence and financialization. The model features quadratic self-amplification in both AI capability ($\lambda A^2$) and financial capital ($\gamma_F K_f^2$), coupled through investment flows. It is shown that under mild conditions, the system exhibits a finite-time singularity where AI capability, AI capital, and financial capital diverge. Near the singularity, the wealth ratio between capital owners and workers diverges super-exponentially, with financialization amplifying the exponent by a factor $\gamma_F/\eta$. Introducing taxes on AI returns ($\tau_{ai}$) and financial gains ($\ta... More >

This paper explores heat transfer and MHD flow of different shapes of (Ag-TiO$_{2}$/PAO Oil) hybrid nanoparticles through an unsteady radially stretching sheet consider variable thermal conductivity and viscosity. The present investigation explores the thermal radiation impact of different shapes (platelet, sphere, brick, blade, cylinder) of hybrid nanoparticles with variable viscosity($\mu_\mathrm{hnf}$) and thermal conductivity($k_\mathrm{hnf}$) under the suction and partial slip parameter. This study presents a novel analysis of variable thermal conductivity and viscosity for different shapes of hybrid nanoparticles. The nonlinear ODEs are generated by proper transformation from governing... More >

A unified fractional simplest equation framework is developed for nonlinear power-law wave equations whose travelling-wave reductions lead to $U'' + \lambda U^p = 0$, $p>1$. In contrast to classical simplest equation methods restricted to integer polynomial expansions, we introduce a fractional power ansatz $U(\xi)=A\phi^\alpha(\xi)$ derived from a dominant balance principle. A general scaling theorem is established, proving that the admissible travelling-wave exponents are uniquely determined by $\alpha(p-1)=2$, yielding the explicit fractional law $\alpha=\frac{2}{p-1}$. Consequently, the equation admits algebraic travelling waves of the universal form $U(\xi)=A(\mu\xi+C_0)^{-2/(p-1)}$, wi... More >