王晚生

2026

High-accuracy approximation of multi-dimensional fractional Laplacian by mixed fractional interpolation

Journal of Computational Physics

DOI

2026

Residual-Based a Posteriori error Analysis and Adaptive Computation for Implicit Euler Method for Nonlinear Neutral Delay Differential Equations

Journal of Scientific Computing

DOI

2026

High-order structure-preserving implicit-explicit Runge-Kutta methods with Lagrange multiplier approach for conservative nonlinear evolution equations

Communications in nonlinear science & numerical simulation

DOI

2026

A Novel and Highly Accurate Node-Type Quadrature Approach for Fractional Laplacian and its Application in Numerically Solving Fractional Poisson Equation

Communications in Computational Physics

DOI

2026

An adaptive integrating factor midpoint method for second order evolution equations

arXiv.org

DOI

2026

A posteriori error estimates of the fully discrete approximations for time fractional parabolic differential equations

Journal of Computational and Applied Mathematics

DOI

2026

Uniform error estimate of Runge-Kutta fully discrete continuous data assimilation algorithms for semilinear reaction-diffusion equations

Applied Numerical Mathematics

DOI

2026

Discrete‐in‐Time Data Assimilation for Reaction–Diffusion Models Using the Delay Sparse Data

Studies in Applied Mathematics

DOI

2025

求解Merton和Kou跳跃扩散模型下美式期权定价的隐显方法

《计算数学》

2025

High Order Methods for Nonlinear Evolution Equations Governed by Semibounded or Dissipative Operators in Normed Space

Journal of Scientific Computing

DOI

2025

Deep Learning Numerical Methods for High-Dimensional Quasilinear PIDEs and Coupled FBSDEs with Jumps

SIAM Journal on Scientific Computing

DOI

2025

Error estimates of general linear and spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian

Computational and Applied Mathematics

DOI

2025

Exponential contractivity and error estimates of IMEX Euler method for nonlinear perturbed dissipative systems in seminormed space

Journal of Computational and Applied Mathematics

DOI

2025

Error Estimates of Operator Splitting Spectral Method for Semiclassical Sub-Diffusive Gross-Pitaevskii Equation

CSIAM Transactions on Applied Mathematics

DOI

2025

Error Analysis of Fully Discrete Data Assimilation Algorithms for Reaction-Diffusion Equation

Advances in Applied Mathematics and Mechanics

DOI

2025

High order semi-IMEX BDF schemes for nonlinear partial integro-differential equations arising in finance

ESAIM: Mathematical Modelling and Numerical Analysis

DOI

2025

Diagonally Implicit Runge-Kutta Methods for Nonlinear Dissipative Systems under Convex Functional in Vector Space

Advances in Applied Mathematics and Mechanics

DOI

2025

Postprocessing mixed finite element methods for the Cahn–Hilliard equation: the fully discrete case

Calcolo

DOI

2025

Fully Discrete Continuous Data Assimilation Algorithms for Semilinear Parabolic Equations with Small Noisy Data

SIAM Journal on Applied Dynamical Systems

DOI

2025

A Second‐Order Variable Step‐Size IMEX Method for American Option Under Jump–Diffusion Model

Mathematical methods in the applied sciences

DOI

2025

Implicit–explicit high-order methods for pricing options under Merton’s jump-diffusion models

Journal of Applied Mathematics and Computation

DOI

2025

Laguerre neural network for solving neutral delay differential equations based on the extreme learning machine

International Journal of Computer Mathematics

DOI

2024

A posteriori error estimates for fully discrete finite difference method for linear parabolic equations

Applied Numerical Mathematics

DOI

2024

Adaptive option pricing based on a posteriori error estimates for fully discrete finite difference methods

Journal of Computational and Applied Mathematics

DOI

2024

Nonsmooth data error estimates for fully discrete finite element approximations of semilinear parabolic equations in Banach space

Journal of Computational and Applied Mathematics

DOI

2024

IMEX variable step-size Runge-Kutta methods for parabolic integro-differential equations with nonsmooth initial data

Communications in Mathematical Sciences

DOI

2024

Robust Error Estimates for Second‐Order Stabilization Finite Element Method for Navier–Stokes Equations With Small Viscosity and Nonsmooth Initial Data

Numerical Methods for Partial Differential Equations

DOI

2024

A Posteriori Error Estimates for Exponential Midpoint Integrator Finite Element Method for Parabolic Equations

Mathematical methods in the applied sciences

DOI

2024

Reconstruction-Based a Posteriori Error Estimates for the L1 Method for Time Fractional Parabolic Problems

Journal of Computational Mathematics

DOI

2024

Adaptive fast L1 − 2 scheme for solving time fractional parabolic problems

Computers & Mathematics with Applications

DOI

2024

A posteriori error estimates for the exponential midpoint method for linear and semilinear parabolic equations

Numerical Algorithms

DOI

2024

Sharp analysis of L1−2 method on graded mesh for time fractional parabolic differential equation

Applied Mathematics Letters

DOI

2023

Efficient Stability-Preserving Numerical Methods for Nonlinear Coercive Problems in Vector Space

SIAM Journal on Numerical Analysis

DOI

2023

Comparison of implicit–explicit and Newton linearized variable two-step BDF methods for semilinear parabolic equations

Computational and Applied Mathematics

DOI

2023

Stability and Convergence of Stepsize-Dependent Linear Multistep Methods for Nonlinear Dissipative Evolution Equations in Banach Space

Journal of Computational Mathematics

DOI

2023

A variable step‐size extrapolated Crank–Nicolson method for option pricing under stochastic volatility model with jump

Mathematical methods in the applied sciences

DOI

2023

Implicit Runge‐Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian

Numerical Methods for Partial Differential Equations

DOI

2023

Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms

Inverse Problems

DOI

2023

Unconditional long-time stability-preserving second-order BDF fully discrete method for fractional Ginzburg-Landau equation

Numerical Algorithms

DOI

2023

Cost-reduction implicit exponential Runge–Kutta methods for highly oscillatory systems

Journal of Mathematical Chemistry

DOI

2022

求解跳-扩散期权定价方程的隐显Runge-Kutta方法

《上海师范大学学报(自然科学版中英文)》

2022

非线性中立型泛函微分方程理论及数值分析

《科学出版社》

2022

带跳随机波动率模型的高阶ADI分裂格式

《计算数学》

2022

Delay-dependent elliptic reconstruction and optimal L∞ (L2) a posteriori error estimates for fully discrete delay parabolic problems

Mathematics of Computation

DOI

2022

Optimal a posteriori estimators for the variable step-size BDF2 method for linear parabolic equations

Journal of Computational and Applied Mathematics

DOI

2022

An efficient IMEX method for nonlinear functional differential equations with state-dependent delay

Applied Numerical Mathematics

DOI

2022

A Posteriori Error Control and Adaptivity for the IMEX BDF2 Method for PIDEs with Application to Options Pricing Models

Journal of Scientific Computing

DOI

2022

Analytical and numerical dissipativity for the space-fractional Allen-Cahn equation

Mathematics and Computers in Simulation

DOI

2022

Stage-based interpolation Runge–Kutta methods for nonlinear Volterra functional differential equations

Calcolo

DOI

2022

Lie-Trotter operator splitting spectral method for linear semiclassical fractional Schrödinger equation

Computers and Mathematics with Applications

DOI

2022

IMEX Runge-Kutta method for solving jump-diffusion option pricing equation

DOAJ (DOAJ: Directory of Open Access Journals)

DOI

2021

Long time Hsα stability of a classical scheme for Cahn-Hilliard equation with polynomial nonlinearity

Applied Numerical Mathematics

DOI

2021

An efficient difference scheme for time-fractional KdV equation

Computational and Applied Mathematics

DOI

2021

Linearly implicit variable step-size BDF schemes with Fourier pseudospectral approximation for incompressible Navier-Stokes equations

Applied Numerical Mathematics

DOI

2021

Two-grid finite element methods for nonlinear time-fractional parabolic equations

Numerical Algorithms

DOI

2021

An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional Sine-Gordon equations

Mathematics and Computers in Simulation

DOI

2021

Dissipativity of variable-stepsize Runge-Kutta methods for nonlinear functional differential equations with application to Nicholson's blowflies models

Communications in nonlinear science & numerical simulation

DOI

2021

An efficient variable step-size method for options pricing under jump-diffusion models with nonsmooth payoff function

ESAIM: Mathematical Modelling and Numerical Analysis

DOI

2020

中立型比例延迟微分系统线性θ-方法的渐近估计

《计算数学》

2020

2个数学模型下的铜期权定价比较

《吉首大学学报(自然科学版)》

DOI

2020

A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay

Journal of Scientific Computing

DOI

2020

Efficient exponential splitting spectral methods for linear Schrödinger equation in the semiclassical regime

DOI

2020

Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations

Advances in Computational Mathematics

DOI

2019

An Efficient Algorithm for Options Under Merton's Jump-Diffusion Model on Nonuniform Grids

Computational Economics，Vol. 530, No. 4

DOI

2019

Hale中立型延迟微分方程的耗散性:新的准则及其应用

《应用数学学报》

2019

Allen-Cahn方程隐式Euler格式的长时间稳定性

《湖南理工学院学报(自然科学版)》

DOI

2019

一类变延迟中立型微分方程梯形方法的渐近估计

《数学物理学报》

2019

Riesz空间分数阶非线性薛定谔方程的一种高效解法

《湖南理工学院学报(自然科学版)》

DOI

2019

Numerical solutions of SDEs with Markovian switching and jumps under non-Lipschitz conditions

Journal of Computational and Applied Mathematics

DOI

2019

On the Variable Two-Step IMEX BDF Method for Parabolic Integro-differential Equations with Nonsmooth Initial Data Arising in Finance

SIAM Journal on Numerical Analysis

DOI

2019

Optimal convergence orders of fully geometric mesh one-leg methods for neutral differential equations with vanishing variable delay

Advances in Computational Mathematics

DOI

2019

An IMEX‐BDF2 compact scheme for pricing options under regime‐switching jump‐diffusion models

Mathematical methods in the applied sciences

DOI

2018

非线性中立型变延迟微分方程的长时间稳定性

《数学物理学报》

2018

求解Merton跳扩散模型的隐显BDF2方法

《湖南理工学院学报(自然科学版)》

2018

Cahn-Hilliard方程的隐显BDF2方法

《湖南理工学院学报(自然科学版)》

2018

A Posteriori Error Analysis for Crank-Nicolson-Galerkin Type Methods for Reaction-Diffusion Equations with Delay

SIAM Journal on Scientific Computing

DOI

2018

A multi-domain Legendre spectral collocation method for nonlinear neutral equations with piecewise continuous argument

International Journal of Computational Mathematics

DOI

2018

Two-grid economical algorithms for parabolic integro-differential equations with nonlinear memory

Applied Numerical Mathematics

DOI

2017

延迟抛物型方程二阶BDF方法的稳定性和后验误差估计

《数学理论与应用》

2017

抛物型方程变步长BDF2方法的后验误差估计

《数学理论与应用》

2017

Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations

Journal of Computational and Applied Mathematics

DOI

2017

Fast numerical valuation of options with jump under Merton's model

Journal of Computational and Applied Mathematics

DOI

2017

Dissipativity of the linearly implicit Euler scheme for Navier‐Stokes equations with delay

DOI

2017

Fully-geometric mesh one-leg methods for the generalized pantograph equation: Approximating Lyapunov functional and asymptotic contractivity ☆

DOI

2017

On A-stable one-leg methods for solving nonlinear Volterra functional differential equations

Applied Mathematics and Computation

DOI

2016

非线性Black-Scholes期权定价模型的数值模拟

《湖南理工学院学报(自然科学版)》

2016

The asymptotic behaviour of the θ-methods with constant stepsize for the generalized pantograph equation

International Journal of Computational Mathematics

DOI

2015

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

Journal of Scientific Computing

DOI

2015

An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation

DOI

2015

On the numerical solution of nonlinear option pricing equation in illiquid markets

Computers and Mathematics with Applications

DOI

2015

High order stable Runge–Kutta methods for nonlinear generalized pantograph equations on the geometric mesh ☆

DOI

2014

Asymptotic stability of solution to nonlinear neutral and Volterra functional differential equations in Banach spaces

Applied Mathematics and Computation

DOI

2014

An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs

TheScientificWorldJournal

DOI

2014

Nonlinear stability of one-leg methods for neutral Volterra delay-integro-differential equations

Mathematics and Computers in Simulation

DOI

2013

非线性中立型泛函微分方程Runge-Kutta法的稳定性和收敛性

《中国科学:数学》

2013

Long-time behavior of the two-grid finite element method for fully discrete semilinear evolution equations with positive memory

Journal of Computational and Applied Mathematics

DOI

2013

Stability of solutions of nonlinear neutral differential equations with piecewise constant delay and their discretizations

Applied Mathematics and Computation

DOI

2013

Stability and convergence of Runge-Kutta methods for nonlinear neutral functional differential equations

DOI

2012

On the One-Leg Methods for Solving Nonlinear Neutral Differential Equations with Variable Delay

Journal of Applied Mathematics

DOI

2012

Contractivity and exponential stability of solutions to nonlinear neutral functional differential equations in banach spaces

Acta Mathematicae Applicatae Sinica (English Series)

DOI

2012

Long time behavior of non-Fickian delay reaction–diffusion equations ☆

DOI

2011

显式和对角隐式Rung-Kutta方法求解中立型泛函微分方程的非线性稳定性

《数值计算与计算机应用》

2011

Asymptotic stability of exact and discrete solutions for neutral multidelay-integro-differential equations

DOI

2011

Implicit–explicit predictor–corrector schemes for nonlinear parabolic differential equations

DOI

2011

Stability Analysis of Runge-Kutta Methods for Nonlinear Neutral Volterra Delay-Integro-Differential Equations

DOI

2010

Preserving stability implicit Euler method for nonlinear Volterra and neutral functional differential equations in Banach space

Numerische Mathematik

DOI

2010

Stability of linear multistep methods for nonlinear neutral delay differential equations in Banach space

Journal of Computational and Applied Mathematics

DOI

2010

Analytical and numerical dissipativity for nonlinear generalized pantograph equations

DOI

2010

A Generalized Halanay Inequality for Stability of Nonlinear Neutral Functional Differential Equations

DOI

2010

Dissipativity and asymptotic stability of nonlinear neutral delay integro-differential equations

DOI

2009

非线性中立型延迟积分微分方程单支方法的收敛性

《中国科学:数学》

2009

Convergence of Runge-Kutta methods for neutral Volterra delay-integro-differential equations

DOI

2009

Conditional contractivity of Runge–Kutta methods for nonlinear differential equations with many variable delays☆

DOI

2009

Convergence of one-leg methods for nonlinear neutral delay integro-differential equations

DOI

2009

Contractivity properties of a class of linear multistep methods for nonlinear neutral delay differential equations

DOI

2009

Stability of one-leg theta-methods for nonlinear neutral differential equations with proportional delay

Applied Mathematics and Computation

DOI

2009

Nonlinear stability of general linear methods for neutral delay differential equations

DOI

2009

Stability of continuous Runge–Kutta-type methods for nonlinear neutral delay-differential equations

DOI

2008

求解非线性中立型延迟微分方程一类线性多步方法的收敛性

《计算数学》

2008

一类线性多步法关于变延迟非线性中立型微分方程的渐近稳定性

《高等学校计算数学学报》

2008

非线性中立型延迟微分方程对角分裂Runge-Kutta法的收缩性

《数值计算与计算机应用》

2008

Stability Analysis of Theta-Methods for Nonlinear Neutral Functional Differential Equations

SIAM Journal on Scientific Computing

DOI

2008

Convergence of waveform relaxation methods for neutral delay differential equations

Mathematical and computer modelling

DOI

2008

Nonlinear stability and asymptotic stability of implicit Euler method for stiff Volterra functional differential equations in Banach spaces

Applied Mathematics and Computation

DOI

2008

Dissipativity of Runge-Kutta methods for neutral delay differential equations with piecewise constant delay

Applied Mathematics Letters

DOI

2008

Nonlinear stability of Runge-Kutta methods for neutral delay differential equations

DOI

2008

Dissipativity of theta-methods for a class of nonlinear neutral delay differential equations

Applied Mathematics and Computation

DOI

2008

Generalized Halanay inequalities for dissipativity of Volterra functional differential equations

DOI

2008

Nonlinear stability of one-leg methods for delay differential equations of neutral type

DOI

2008

Nonlinear stability of explicit and diagonally implicit Runge-Kutta methods for neutral delay differential equations in Banach space

Applied Mathematics and Computation

DOI

2008

Nonlinear stability of theta-methods for neutral differential equations in Banach space

Applied Mathematics and Computation

DOI

2007

On the one-leg theta-methods for solving nonlinear neutral functional differential equations

Applied Mathematics and Computation

DOI

2006

一类多步方法求解Banach空间中试验问题的非线性稳定性

《计算数学》

2004

求解变延迟微分方程的一类线性多步方法的收缩性

《高等学校计算数学学报》

2004

非线性中立型延迟微分方程稳定性分析

《计算数学》

2022

基于回归模型对沪深300股指期权的定价仿真

《第三十四届中国仿真大会暨第二十一届亚洲仿真会议论文集》

DOI

2025

Recurrent Neural Operators: Stable Long-Term PDE Prediction

arXiv (Cornell University)

DOI

2024

FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equations

arXiv (Cornell University)

DOI