In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown.

The main objective of this study is to introduce a new class of $2q$ -point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs.

In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is used for the time discretization. A numerical example from PDE is used to evaluate the accuracy of the proposed method. The numerical results are evaluated in comparison to the exact solutions. The findings consistently indicate that the suggested technique provides good error estimates. We also discovered that our proposed method was unconditionally stable. Hence, based on the results and the efficiency of the method, the method is suitable for solving heat equation.

In this article, our main purpose is to investigate generalized integral formulas containing the extended Wright type generalized hypergeometric function. Moreover, certain special cases of the main results given here have also been pointed out for the Wright type hypergeometric function.

Marijuana is an illicit narcotic with multiple negative health effects as it continues to pose a severe danger to the health of people in emerging regions. Marijuana is spread through interactions between users and non-users. This study utilizes first-order non-linear ordinary differential equations to modify the Non-user, Experimental, Recreational, and Addicted (NERA) users’ model by adding a new class known as the hospitalized class of marijuana smokers. Moreover, this paper focuses on validating the NERA model using the sensitivity analysis concept. The NERA model presented in a previous study for marijuana usage among the target population consists of four distinct stages: the first stage is known as the non-user stage and is represented by the letter N; the second stage is known as the experimental stage of marijuana smoking and is represented by the letter E; the third stage is known as the recreational stage of marijuana smoking and is represented by the letter R; the fourth stage is represented by the letter A; and this last stage is known as the addicted stage of marijuana smoking. The suggested mathematical method achieved the reproduction number () for marijuana use. The results of the sensitivity tests indicate how crucial a variety of variables are to the spread of marijuana. The parameters that have a key impact on marijuana consumption were discovered based on sensitivity analysis. All these procedures, including the reproductive number and invariant region, using the sensitivity analysis concept were utilized to validate the updated model. In this study, the NERA model is modified by utilizing first-order non-linear ordinary differential equations. Furthermore, as demonstrated by the graphical and technique sections, the proposed modified models were successfully validated for improved performance.

Full waveform inversion (FWI) is a recent powerful method in the area of seismic imaging where it used for reconstructing high-resolution images of the subsurface structure from local measurements of the seismic wavefield. This method consists in minimizing the distance between the predicted and the recorded data. The predicted data are computed as the solution of a wave-propagation problem. In this study, we investigate two algorithms Gauss-Newton and L-BFGS for solving FWI problems. We compare these algorithms in terms of its robustness and speed of convergence. Also, we implement the Tikhonov regularization for assisting convergence. Numerical results show that Gauss-Newton method performs better than L-BFGS method in terms of convergence of \(l_{2}\)-norm of misfit function gradient since it provides better convergence as well as the quality of high resolution constructed images. Yet, L-BFGS outperforms Gauss-Newton in terms of computationally efficiency and feasibility for FWI.