In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

A modify approach for approximating an analytical solution of some PDEs with fractional order is the Variational Adomian decomposition methodology (VIADM). We provide several examples to support our conclusions. the results of the solutions process showed that the suggested approach is highly simple, dependable, and effective. The outcomes demonstrate the effectiveness and accuracy of current technology in solving a variety of applied scientific nonlinear challenges. All of the calculations and visualizations were done using the MATLAB R2024B software. In Caputo Sense, fractional derivatives are mentioned. Additionally, a graphical representation of the solutions to a few cases was created. Solution graphs are displayed for problems

The preparation of the phenanthridine derivative compound was achieved by adopting an efficient one-pot synthetic approach. The condensation of an ethanolic mixture of benzaldehyde, cyclohexanone and ammonium acetate in a 2:1:1 mole ratio resulted in the formation of the title compound. Analytical and spectroscopic techniques were used to confirm the nature of the new compound. A mechanism for the formation of the phenanthridine moiety that is based on three steps has been suggested

Background: Dimensional changes of acrylic denture bases after polymerization results in need for further adjustments or even ends with technical failure of the finished dentures. The purpose of this study was to estimate the linear dimensional changes for different palatal depths when using multiple investment materials and polymerization techniques. Materials and methods: Ninety upper complete denture bases were constructed for this study. They were divided into two main groups according to the polymerization methods: conventional water bath and experimental autoclave (short and long cycles). Each main group was further subdivided into three subgroups according to the palatal depth (shallow, medium and deep). Furthermore, for each palatal

In high-dimensional semiparametric regression, balancing accuracy and interpretability often requires combining dimension reduction with variable selection. This study intro- duces two novel methods for dimension reduction in additive partial linear models: (i) minimum average variance estimation (MAVE) combined with the adaptive least abso- lute shrinkage and selection operator (MAVE-ALASSO) and (ii) MAVE with smoothly clipped absolute deviation (MAVE-SCAD). These methods leverage the flexibility of MAVE for sufficient dimension reduction while incorporating adaptive penalties to en- sure sparse and interpretable models. The performance of both methods is evaluated through simulations using the mean squared error and variable selection cri

This study proposes a new method for designing adaptive routing algorithms for three‐dimensional (3D) networks‐on‐chip (NoCs). This method is based on extending the existing 2D turn model adaptive routing to a 3D scenario. A 3D plane‐balanced approach with maximal degree of adaptiveness is achieved by applying a well‐defined set of rules for different strata of the 3D NoC. The proposed method is applicable to any of the turn models. In this study, the authors employ odd–even turn model as a basis for introducing the proposed strategy. Experimental results show that the new 3D odd–even turn model can achieve up to 28.5% improvement in performance over conventional 3D odd–even approach. The improvement is consistent fo