Based on the Ψ-functions series method, a new numerical integration method for perturbed and damped second-order systems of differential equations is presented. This multistep method is defined for variable step and variable order (VSVO) and main...
The pure pursuit (PP) method has been widely employed in automated guided vehicles (AGVs) to address path tracking challenges. However, the traditional pure pursuit method exhibits certain limitations in tracking performance. For instance, selecting...
If soil hydraulic conductivity or water holding capacity could be measured with a small volume of samples, it would benefit international fields where researchers can only carry a limited amount of soils out of particular regions. We performed a pinh...
Distributed energy resources (DERs) offer a promising solution for enhancing the resilience and efficiency of modern power systems. However, the inherent time delays in their communication and control systems can degrade their small signal stability,...
There are some classes of methods for solving integral equations of the variable boundaries. It is known that each method has its own advantages and disadvantages. By taking into account the disadvantages of known methods, here was constructed a new...
Stiff delay differential equations are frequently utilized in practice, but their numerical simulations are difficult due to the complicated interaction between the stiff and delay terms. At the moment, only a few low-order algorithms offer acceptabl...
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...
We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after m steps) for solving nonlinear equations,
Chaotic oscillators have been designed with embedded systems like field-programmable gate arrays (FPGAs), and applied in different engineering areas. However, the majority of works do not detail the issues when choosing a numerical method and the ass...
Efficient and accurate time integration is essential for simulating combustion processes with stiff, multiscale dynamics arising from diffusion, reaction, and advection interactions. Standard implicit–explicit (IMEX) methods employ a two-additi...
The Volume of Fluid (VOF) method is used in two-phase fluid flow problems of ship hydrodynamic calculations, to capture the motion and distribution of the gas–liquid free surface. To ensure solution stability and accuracy, numerical simulations...
18 March 2019
In this paper, we applied a fractional multi-step differential transformed method, which is a generalization of the multi-step differential transformed method, to find approximate solutions to one of the most important epidemiology and mathematical e...
This paper is dedicated to the development of a novel class of quasi-Newton techniques tailored to address computational challenges posed by memory constraints. Such methodologies are commonly referred to as “limited” memory methods. The...
The novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a ra...
In this paper, we construct two multi-step inertial regularized methods for hierarchical inequality problems involving generalized Lipschitzian and hemicontinuous mappings in Hilbert spaces. Then we present two strong convergence theorems and some nu...
A theory for the calculation of the phase–lag and amplification–factor for explicit and implicit multistep techniques for first–order differential equations was recently established by the author. His presentation also covered how t...
A two-step fifth and a multi-step
When finding numerical solutions to stiff and nonstiff initial value problems using linear multistep methods, ill-conditioned systems are often encountered. In this paper, we demonstrate how this ill-conditioning can be circumvented without iterative...
The local convergence analysis of the multi-step seventh order method to solve nonlinear equations is presented in this paper. The point of this paper is that our proposed study requires a weak hypothesis where the Fréchet derivative of the no...
Recently, the author developed a theory for the computation of the phase lag and amplification factor for explicit and implicit multistep methods for first-order differential equations. In this paper, we will investigate the role of the derivatives o...
The author has just published a theory on first-order differential equations that accounts for the phase-lag and amplification-factor calculations using explicit, implicit, and backward differentiation multistep methods. Eliminating the phase-lag and...
In this study, the influence of the multi-step heating methods, such as two-step heating methods and three-step heating methods, on the properties of Al–Si coating boron steel sheet were evaluated by using the Gleeble-3500 thermal simulator. The evol...
To solve the problem that a parameter search easily falls into a local optimum and the two-dimensional electron density profile construction error is large in the process of backscatter ionogram inversion, an improved method using neighborhood-aided...
The egg production rate is a crucial metric in animal breeding, subject to biological and environmental influences and exhibits characteristics of small sample sizes and non-linearity. Currently, egg production rate prediction research predominantly...
Wind energy is highly volatile, and large-scale wind power grid integration significantly impacts grid stability. Accurate forecasting of wind turbine power can improve wind power consumption and ensure the economy of the power grid. This paper propo...
Multistep methods for the numerical solution of ordinary differential equations are an important class of applied mathematical techniques. This paper is motivated by recently reported advances in semi-implicit numerical integration methods, multistep...
In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary...
In this paper, we deal with a new family of iterative methods for approximating the solution of nonlinear systems for non-differentiable operators. The novelty of this family is that it is a m-step generalization of the Steffensen-type method by upda...
In this paper, we compare a multi-step method and a multi-stage method for stiff initial value problems. Traditionally, the multi-step method has been preferred than the multi-stage for a stiff problem, to avoid an enormous amount of computational co...
In the present paper, a fifth-order direct multistep block method is proposed for solving the second-order Delay Differential Equations (DDEs) directly with boundary conditions using constant step size. In many life sciences applications, a delay pla...
This research introduces a fresh methodology for creating efficient numerical algorithms to solve first-order Initial Value Problems (IVPs). The study delves into the theoretical foundations of these methods and demonstrates their application to the...
Developing new and efficient numerical integration techniques is of great importance in applied mathematics and computer science. Among the variety of available methods, multistep ODE solvers are broadly used in simulation software. Recently, semi-im...
In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show...
This study examines the thermal characteristics and kinetics of oil shale combustion using thermogravimetric analysis (TGA) at various heating rates. The combustion process includes three stages: dehydration, main combustion (70–80% mass loss),...
In our paper, we propose two new iterative algorithms with Meir–Keeler contractions that are based on Tseng’s method, the multi-step inertial method, the hybrid projection method, and the shrinking projection method to solve a monotone variational in...
The execution time that takes to perform numerical simulation of a chaotic oscillator mainly depends on the time-step h. This paper shows that the optimization of chaotic oscillators can be enhanced by estimating the highest h in either one-step or m...
This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended met...
Soil moisture prediction is a key parameter for effective irrigation scheduling and water use efficiency. However, accurate long-term prediction remains challenging, as most existing models excel in short- to medium-term prediction but struggle to ca...
We consider an adaptive Adams-type multistep method for the numerical solution of ordinary differential equations based on algebraic, trigonometric, and exponential interpolation (the ATE method). For each interpolation class, the corresponding schem...
In this paper, in order to solve systems of nonlinear equations, a new class of frozen Jacobian multi-step iterative methods is presented. Our proposed algorithms are characterized by a highly convergent order and an excellent efficiency index. The t...
We present a collection of recent results on the numerical approximation of Volterra integral equations and integro-differential equations by means of collocation type methods, which are able to provide better balances between accuracy and stability...
Multistep integration methods are widespread in the simulation of high-dimensional dynamical systems due to their low computational costs. However, the stability of these methods decreases with the increase of the accuracy order, so there is a known...
It is very meaningful and challenging to efficiently seek common solutions to operator systems (CSOSs), which are widespread in pure and applied mathematics, as well as some closely related optimization problems. The purpose of this paper is to intro...
This paper addresses the numerical integration of first-order ordinary differential equations by developing a continuous linear multistep block method. The method is constructed through the approximation of the exact solution using a linear combinati...
In this article, we introduce a new inertial multi-step regularized generalized Popov’s extra-gradient method to solve the hierarchical variational inequality problem (HVIP). We extend the previous Lipschitzian and strongly monotone mapping to...
Research on topological interlocking (TI) assemblies indicates that the geometry of blocks plays a significant role in the performance of a configuration. The current TI generation methods can return assemblies of uniform antiprisms, tetrahedra, cube...
We study three multistep implicit–explicit (IMEX) time discretizations coupled with a local discontinuous Galerkin (LDG) spatial discretization for a class of one-dimensional nonlinear fourth-order partial differential equations (PDEs), with pa...
Multistep methods typically use Taylor series to attain their convergence order, which necessitates the existence of derivatives not naturally present in the iterative functions. Other issues are the absence of a priori error estimates, information a...
Real-time computational capability for simultaneous grasping force and displacement determination constitutes a critical enabler for stable and reliable grasping performance in dexterous robotic grasping. To accelerate the computational efficiency of...
Numerical methods for the solution of ordinary differential equations are based on polynomial interpolation. In 1952, Brock and Murray have suggested exponentials for the case that the solution is known to be of exponential type. In 1961, Gautschi ca...
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