In this paper, we present three improvements to a three-point third order variant of Newton’s method derived from the Simpson rule. The first one is a fifth order method using the same number of functional evaluations as the third order method, the s...
Numerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: Simpson’s 13 rule or Simpson’s quadrature formula and Simpson’s 38 rule or Simpson’s second...
Simpson’s rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities...
In this article we give a variant of the Hermite–Hadamard integral inequality for twice differentiable functions. It represents an improvement of this inequality in the case of convex/concave functions. Sharp two-sided inequalities for Simpson&...
In this paper, two theorems are explained which are used in order to find the improper integral I = ({int_a^infty})f(x)dx numerically. It has been proved in [4], one can use the Trapezoidal and Simpson rules to find the definite integral Im = ({int_a...
In this work, a perturbed Milne’s quadrature rule for n-times differentiable functions with Lp-error estimates is derived. One of the most important advantages of our result is that it is verified for p-variation and Lipschitz functions. Severa...
This study aims to compare two approaches for the reserve calculation of cement raw material by geological sections and structural maps. The first is legally based, and its accuracy is approved by periodical calculation of the exploited material on s...
This paper focuses on computational technique to solve linear systems of Volterra integro-fractional differential equations (LSVIFDEs) in the Caputo sense for all fractional order linsin0,1 using two and three order block-by-block approach with expli...
Emptying processes are operations frequently required in hydraulic installations by water utilities. These processes can result in drops to sub-atmospheric pressure pulses, which may lead to pipeline collapse depending on soil characteristics and the...
We propose several improvements of the Hermite–Hadamard inequality in the form of linear combination of its end-points and establish best possible constants. Improvements of a second order for the class Φ ( I ) with applications in...
A composition is a powerful tool for obtaining new numerical methods for solving differential equations. Composition ODE solvers are usually based on single-step basic methods applied with a certain set of step coefficients. However, multistep compos...
In this paper, we study the problem of solving Seal’s type partial integro-differential equations (PIDEs) for the classical compound Poisson risk model. A data-driven deep neural network (DNN) method is proposed to calculate finite-time surviva...
In this paper, we give some correct quantum type Simpson’s inequalities via the application of q-Hölder’s inequality. The inequalities of this study are compatible with famous Simpson’s 1/8 and 3/8 quadrature rules for four and...
In this paper, we analyze the q-iterative schemes to determine the roots of nonlinear equations by applying the decomposition technique with Simpson’s 13-rule in the setting of q-calculus. We discuss the convergence analysis of our suggested it...
In this study, we introduce a new hybrid identity that effectively combines Newton–Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson’s second rule and the left- and right-Radau two-point rules, among o...
Elastic recovery of the material, called springback, is one of the problems in sheet metal forming of drawpieces, especially with a complex shape. The springback can be influenced by various technological, geometrical, and material parameters. In thi...
Fractional calculus has been a concept used to acquire new variants of some well-known integral inequalities. In this study, our primary goal is to develop majorized fractional Simpson’s type estimates by employing a differentiable function. Pr...
In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalu...
In this paper, we investigate a class of fuzzy partially differentiable models for Caputo–Hadamard-type Goursat problems with generalized Hukuhara difference, which have been widely recognized as having a significant role in simulating and anal...
This paper presents new integral inequalities for differentiable generalized convex functions in the second sense, with a focus on improving the accuracy of Weddle’s formula for numerical integration. The study is motivated by the following thr...
Some recent results have been found treating the famous Simpson’s rule in connection with the convexity property of functions and those called generalized convex. The purpose of this article is to address Newton-type integral inequalities by as...
Integral inequalities are a powerful tool for estimating errors of quadrature formulas. In this study, some symmetric dual Simpson type integral inequalities for the classes of s-convex, bounded and Lipschitzian functions are proposed. The obtained r...
Distributed-order, space-fractional diffusion equations are used to describe physical processes that lack power-law scaling. A fourth-order-accurate, A-stable time-stepping method was developed, analyzed, and implemented to solve inhomogeneous parabo...
A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a m...
The best Weibull distribution methods for the assessment of wind energy potential at different altitudes in desired locations are statistically diagnosed in this study. Seven different methods, namely graphical method (GM), method of moments (MOM), s...
Modification of the cotton canopy results in shade avoidance and competition for light, which shows that density and spatial arrangement of cotton have a great impact on light interception. This experiment was conducted in 2018 and 2019 in the experi...
This paper presents a control method for achieving precise robotic contact on complex and curved surfaces in manufacturing and automation. The method combines smooth trajectory planning with contact force control to improve finishing accuracy while r...
Aside from languages having no form of written expression, it is usually the case with every language on this planet that texts are written in a single character. But every rule has its exceptions. A very rare exception is Japanese, the texts of whic...
The CESTAC (Control et Estimation STochastique des Arrondis de Calculs) method is based on a probabilistic approach of the round-off error propagation which replaces the floating-point arithmetic by the stochastic arithmetic. This is an efficient met...
This paper introduces a new class of Newton-type inequalities (NTIs) within the framework of extended fractional integral operators. This study begins by establishing a fundamental identity for generalized fractional Riemann–Liouville (FR-L) op...
This article introduces the Third Space of Indian child welfare to theorize how Indigenous nations simultaneously engage and disrupt settler legal systems while building sovereign, care-based alternatives. Drawing from legal analysis, Indigenous poli...
Invoking the matrix transfer technique, we propose a novel numerical scheme to solve the time-fractional advection–dispersion equation (ADE) with distributed-order Riesz-space fractional derivatives (FDs). The method adopts the midpoint rule to...
This study presents an efficient high-order radius function Hermite finite difference (RBF-HFD) scheme for the numerical solution of Caputo time-fractional sub-diffusion equations with integral boundary conditions. The spatial derivatives are approxi...
Urban informality in developing economies like South Africa takes two forms: freestanding shacks are built in informal settlements, and backyard shacks are built in the yard of a formal house. The latter is evident in established townships around Sou...
Background. Left ventricle (LV) global longitudinal strain (GLS) at rest has shown prognostic value in patients (pts) with severe aortic stenosis (SAS). Contractile reserve (CR) during exercise stress echo (ESE) estimated via GLS (CR-GLS) could bette...
Identifying the ideal plant nature and canopy structure is of great importance for improving photosynthetic production and the potential action of plants. To address this challenge, an investigation was accomplished in 2018 and 2019 at the Institute...
The non-unique critical state represents the distance between the critical state line (CSL) and the isotropic consolidation line (ICL) that significantly varies with stress paths and particle size distribution of soils. A structural bounding surface...
Elevational gradients provide an excellent opportunity to assess biodiversity patterns and community structure. Previous studies mainly focus on higher elevations or are limited to small areas in mountainous regions. Little information can be found o...
The change grassland plant communities demonstrate with elevation has been one of the hot issues in ecological research, and there remain many unsolved problems. In order to further elucidate the rules of grassland plant community change with elevati...
Background: Two-dimensional volumetric exercise stress echocardiography (ESE) provides an integrated view of left ventricular (LV) preload reserve through end-diastolic volume (EDV) and LV contractile reserve (LVCR) through end-systolic volume (ESV)...