A5061268303- Fractional Differential Equations Solutions
- Differential Equations and Numerical Methods
- Complex Systems and Time Series Analysis
- Financial Risk and Volatility Modeling
- Nonlinear Differential Equations Analysis
- Stochastic processes and financial applications
- Fractal and DNA sequence analysis
- Machine Learning in Bioinformatics
- Numerical methods in engineering
- Genomics and Phylogenetic Studies
- Numerical methods for differential equations
- Iterative Methods for Nonlinear Equations
- Image and Signal Denoising Methods
- Probabilistic and Robust Engineering Design
- Soil Geostatistics and Mapping
- Chaos control and synchronization
- Protein Structure and Dynamics
- RNA and protein synthesis mechanisms
- Nanofluid Flow and Heat Transfer
- Mathematical Dynamics and Fractals
- Analytic and geometric function theory
- Stochastic processes and statistical mechanics
- Probability and Risk Models
- Statistical Methods and Inference
- Hydrology and Drought Analysis
Queensland University of Technology
2014-2024
Swinburne University of Technology
2018-2024
Xiangtan University
2001-2020
Chinese University of Hong Kong
2020
Hunan Agricultural University
2020
University of Central Florida
2005-2014
Cardiff University
2010
Taras Shevchenko National University of Kyiv
2010
Muroran Institute of Technology
2002
Australian National University
2000-2001
In this paper, we consider a variable-order fractional advection-diffusion equation with nonlinear source term on finite domain. Explicit and implicit Euler approximations for the are proposed. Stability convergence of methods discussed. Moveover, also present method lines, matrix transfer technique, an extrapolation equation. Some numerical examples given, results demonstrate effectiveness theoretical analysis.
A physical-mathematical approach to anomalous diffusion is based on a generalized equation containing derivatives of fractional order. In this paper, an subdiffusion (ASub-DE) considered. new implicit numerical method (INM) and two solution techniques for improving the order convergence INM solving ASub-DE are proposed. The stability investigated by energy method. Some examples given. results demonstrate effectiveness theoretical analysis. These methods supporting can also be applied other...
In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component discretized by Crank--Nicolson method. detailed implementation of presented. stability and convergence analysis strictly proven, which shows that derived stable convergent order $2$ in time. An optimal error estimate also obtained introducing orthogonal projector. present extended to...
The inherent heterogeneities of many geophysical systems often gives rise to fast and slow pathways water chemical movement. One approach model solute transport through such media is by fractional diffusion equations with a space–time dependent variable coefficient. In this paper, two-sided space coefficient nonlinear source term subject zero Dirichlet boundary conditions considered. Some finite volume methods solve differential equation constant dispersion have been proposed. spatial...
In this paper, we consider a variable-order anomalous subdiffusion equation. A numerical scheme with first order temporal accuracy and fourth spatial for the equation is proposed. The convergence, stability, solvability of are discussed via technique Fourier analysis. Another improved second also Some examples given, results demonstrate effectiveness theoretical
The fractional Fokker--Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the nonlocal property derivative interesting problem to explore high accuracy numerical methods differential equations. In this paper, a space-time spectral method presented solution time initial-boundary value problem. proposed employs Jacobi polynomials temporal discretization and Fourier-like basis functions spatial discretization. Due diagonalizable...