This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

       Finally, all algori

This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm th

This study depicts the removal of Manganese ions (Mn²⁺) from simulated wastewater by combined electrocoagulation/ electroflotation technologies. The effects of initial Mn concentration, current density (C.D.), electrolysis time, and different mesh numbers of stainless steel screen electrodes were investigated in a batch cell by adopting Taguchi experimental design to explore the optimum conditions for maximum removal efficiency of Mn. The results of multiple regression and signal to noise ratio (S/N) showed that the optimum conditions were Mn initial concentration of 100 ppm, C.D. of 4 mA/cm², time of 120 min, and mesh no. of 30 (wire/inch). Also, the relative significance of each factor was attained by the analysis

This study depicts the removal of Manganese ions (Mn2+) from simulated wastewater by combined electrocoagulation/ electroflotation technologies. The effects of initial Mn concentration, current density (C.D.), electrolysis time, and different mesh numbers of stainless steel screen electrodes were investigated in a batch cell by adopting Taguchi experimental design to explore the optimum conditions for maximum removal efficiency of Mn. The results of multiple regression and signal to noise ratio (S/N) showed that the optimum conditions were Mn initial concentration of 100 ppm, C.D. of 4 mA/cm2, time of 120 min, and mesh no. of 30 (wire/inch). Also, the relative significance of each factor was attained by the analysis of variance (ANO

For aspirin estimated, a molecularly imprinted polymer MIP-ASP electrodes were generated by electro-polymerization process, the electrodes were prepared by combining the template (aspirin) with (vinyl acetate (VA), 1-vinylimidizole (VIZ) as a functional monomer and N, N-methylene bisacrylamide (MBAA) as crosslinkers using benzoyl peroxide (BPO) as an initiator. The efficiency of the membrane electrodes was analyzed by differential pulse voltammetry (DPV). Four electrodes were synthesized using two different plasticizers, di-butyl sebacate (DBS), di-octyl phthalate (DOP) in PVC matrix. Scanning electron microscopy (SEM) was used to describe the generated MIP, studying the electrodes properties, the slope, detection limit, and life

          A novel median filter based on crow optimization algorithms (OMF) is suggested to reduce the random salt and pepper noise and improve the quality of the RGB-colored and gray images. The fundamental idea of the approach is that first, the crow optimization algorithm detects noise pixels, and that replacing them with an optimum median value depending on a criterion of maximization fitness function. Finally, the standard measure peak signal-to-noise ratio (PSNR), Structural Similarity, absolute square error and mean square error have been used to test the performance of suggested filters (original and improved median filter) used to removed noise from images. It achieves the simulation based on MATLAB R2019b and the resul

In this article, the high accuracy and effectiveness of forecasting global gold prices are verified using a hybrid machine learning algorithm incorporating an Adaptive Neuro-Fuzzy Inference System (ANFIS) model with Particle Swarm Optimization (PSO) and Gray Wolf Optimizer (GWO). The hybrid approach had successes that enabled it to be a good strategy for practical use. The ARIMA-ANFIS hybrid methodology was used to forecast global gold prices. The ARIMA model is implemented on real data, and then its nonlinear residuals are predicted by ANFIS, ANFIS-PSO, and ANFIS-GWO. The results indicate that hybrid models improve the accuracy of single ARIMA and ANFIS models in forecasting. Finally, a comparison was made between the hybrid foreca