Search results

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain.

For positive and bounded initial data, the authors study the initial zero-boundary value problem.

The findings of this study showed the complete extinction of a continuous weak solution at a finite time.

The extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian.

The purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.

This study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.

The stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.

In this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.

With the development of machine learning techniques, the artificial intelligence systems such as crowd networks are becoming more autonomous and smart. Therefore, there is a growing demand for developing a universal intelligence measurement so that the intelligence of artificial intelligence systems can be evaluated. This paper aims to propose a more formalized and accurate machine intelligence measurement method.

This paper proposes a quality–time–complexity universal intelligence measurement method to measure the intelligence of agents.

By observing the interaction process between the agent and the environment, we abstract three major factors for intelligence measure as quality, time and complexity of environment.

This paper proposes a calculable universal intelligent measure method through considering more than two factors and the correlations between factors which are involved in an intelligent measurement.

This study aims to develop an automatic lane-change mechanism on highways for self-driving articulated trucks to improve traffic safety.

The authors proposed a novel safety lane-change path planning and tracking control method for articulated vehicles. A double-Gaussian distribution was introduced to deduce the lane-change trajectories of tractor and trailer coupling characteristics of intelligent vehicles and roads. With different steering and braking maneuvers, minimum safe distances were modeled and calculated. Considering safety and ergonomics, the authors invested multilevel self-driving modes that serve as the basis of decision-making for vehicle lane-change. Furthermore, a combined controller was designed by feedback linearization and single-point preview optimization to ensure the path tracking and robust stability. Specialized hardware in the loop simulation platform was built to verify the effectiveness of the designed method.

The numerical simulation results demonstrated the path-planning model feasibility and controller-combined decision mechanism effectiveness to self-driving trucks. The proposed trajectory model could provide safety lane-change path planning, and the designed controller could ensure good tracking and robust stability for the closed-loop nonlinear system.

This is a fundamental research of intelligent local path planning and automatic control for articulated vehicles. There are two main contributions: the first is a more quantifiable trajectory model for self-driving articulated vehicles, which provides the opportunity to adapt vehicle and scene changes. The second involves designing a feedback linearization controller, combined with a multi-objective decision-making mode, to improve the comprehensive performance of intelligent vehicles. This study provides a valuable reference to develop advanced driving assistant system and intelligent control systems for self-driving articulated vehicles.

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.