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Purpose: In this study, first, second, third, and fourth-order derivative spectrophotometric methods utilizing the peak—zero (P—O) and peak-peak (P—P) techniques of measurement were developed for the determination of levofloxacin, norfloxacin, and moxifloxacin. These methods were applied to their combined pharmaceutical dosage form or individually for levofloxacin, norfloxacin, and moxifloxacin. Methods: Linearity was established in the concentration range of 2–20 µg/mL. The procedures are simple, quick, and precise. The developed methods are sensitive, accurate, and cost-effective, demonstrating excellent correlation coefficients (R2 = 0.9998) and mean recovery values ranging from 99.20% to 100.08%, indicating a high level of precision. Results: The developed approach was effectively employed to determine the levofloxacin, norfloxacin, and moxifloxacin content in commercially available pharmaceutical dosages. Conclusions: Statistical analysis and recovery tests confirmed the method's linearity and accuracy. The results suggest that this method can be utilized for routine analysis in both bulk and commercial formulations. The simplicity, accuracy, and cost-effectiveness of the developed methods make them valuable for pharmaceutical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose a robust and simple technique with efficient algorithmic implementation for numerically solving the nonlocal evolution problems. A theta-type (θ -type) convolution quadrature rule is derived to approximate the nonlocal integral term in the problem under consideration, such that θ ∈ (1 2 , 1) , which remains untreated in the literature. The proposed approaches are based on the θ method ( 1 2 ≤ θ ≤ 1 ) for the time derivative and the constructed θ -type convolution quadrature rule for the fractional integral term. A detailed error analysis of the proposed scheme is provided with respect to the usual convolution kernel and the tempered one. In order to fully discretize our problem, we implement the orthogonal spline collocation (OSC) method with piecewise Hermite bicubic for spatial operators. Stability and error estimates of the proposed θ -OSC schemes are discussed. Finally, some numerical experiments are introduced to demonstrate the efficiency of our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we provide a numerical solution for the nonlinear tempered fractional integrodifferential equation in three dimensions. We use the trapezoidal convolution rule with backward differences (BDF2) for temporal discretization, and develop an alternating direction implicit difference scheme for spatial discretization. A novel fast approximation is applied to tackle the nonlinear term. The stability and convergence analysis of the numerical scheme are analyzed. Furthermore, some numerical experiments are provided to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

This manuscript deals with a space-fractional generalized wave problem involving the fractional Laplacian operator of order α for 1 < α ≤ 2 . We propose an accurate numerical method to solve the mentioned fractional wave problem. The problem is discretized in spatial direction by the Fourier spectral method, and in temporal direction by using the fourth-order exponential time-differencing Runge–Kutta method. One of the main features of this method is reducing the mentioned fractional wave model to an ODE by using the Fourier transform. Then the fourth-order exponential time-differencing Runge–Kutta method is used to solve this ODE. We define the discrete energy function and check the energy-conserving properties. The convergence of this method is proved. Various numerical experiments are conducted to confirm the accuracy and dependability of the suggested approach. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the nonlinear fractional pseudo‐parabolic equations (FPPEs). We propose an accurate numerical algorithm for solving the aforementioned well‐known equation. The problem is discretized in the temporal direction by utilizing a graded mesh linearized scheme and in the spatial direction by the Galerkin‐spectral scheme. We investigate the stability conditions of the proposed scheme. We also provide an H1$$ {H}^1 $$ error estimate of the proposed approach to demonstrate that it is convergent with temporal second‐order accuracy for fitted grading parameters. The proposed scheme is also extended to tackle coupled FPPEs. Numerical experiments are provided to validate the accuracy and reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]