141 papers
This paper proposes and analyzes an eighth-order, one-sixth block multiderivative numerical method based on Chebyshev polynomials and a negative-steps strategy for the direct solution of second-order initial value problems, demonstrating its superior accuracy and stability through theoretical analysis and comparative numerical examples.
This paper demonstrates that numerically converged solutions to saturating semilinear elliptic problems can still yield unreliable Morse indices due to unresolved nodal-layer effects, necessitating a two-resolution workflow that separately verifies branch fidelity and low-spectrum reliability to prevent false stability crossings.
This paper establishes a rigorous multi-level mathematical framework for correlated error accumulation in quantum circuits by proving a central theorem on accumulation scaling, deriving stability and universality results, and validating the model's statistical properties and sample complexity through both analytical proofs and Monte Carlo simulations.
This paper establishes the theoretical distinctions between Caputo and Riemann-Liouville fractional derivatives, demonstrating the former's superiority for biological initial-value problems, and applies this framework to a cancer cell epidemic model to analyze how fractional orders influence memory effects, disease progression, and immunotherapy response.
This paper establishes the boundedness, parametrix construction, and well-posedness of a novel class of non-classical pseudodifferential operators defined by Prabhakar–Fox–Wright symbols with log-oscillatory phases, proving that their associated hyperbolic evolution exhibits derivative loss determined solely by the phase regularity while remaining independent of the special-function envelope, with all analytical results rigorously verified via high-precision numerical computation.
This study characterizes complex balanced equilibria in weakly reversible power law kinetic systems by introducing the PL-TIK decomposition, demonstrating that such systems with weakly reversible, incidence-independent PL-TIK decompositions are complex balanced, and validating these findings through application to Schmitz' Carbon Cycle Model.
This study introduces a q-Legendre spectral framework for solving the Schwarzian KdV equation under Möbius periodic boundary conditions, demonstrating spectral accuracy while diagnosing a genuine, boundary-induced finite-time blow-up mechanism distinct from numerical aliasing errors, with stability characteristics varying non-monotonically across parameter sets representing different atomic lattice structures.
This paper establishes the convergence and localization of Fourier series for functions that are Henstock-Kurzweil integrable but not Lebesgue integrable due to singular behavior at the origin, provided they satisfy specific Dini-type or bounded-variation conditions.
This paper proposes a numerically efficient Itô stochastic differential equation model for multi-site fisheries utilizing Fish Aggregating Devices (FADs) and solves a corresponding stochastic optimization problem to maximize fishing profits by optimally controlling fishing efforts.
This paper proposes a Nash game formulation with Tikhonov regularization to solve the ill-posed elliptic Cauchy problem, establishing explicit, non-asymptotic error bounds for the reconstruction in practical noisy regimes without requiring additional spectral source-type assumptions.