Related references
Note: Only part of the references are listed.
Article
Environmental Sciences
Mohammad Ghani et al.
Summary: The paper studies a fractional mathematical model on diphtheria disease, taking into account parameters such as natural immunity, treatment, and vaccination. The model involves five subpopulations and utilizes Caputo fractional derivative to represent memory effects and long-rate interactions. The paper presents analytical results on concepts of fractional calculus, well-posedness of the model, and stability analysis. Numerical simulations are conducted using the predictor-corrector scheme, and the model is validated with real data using the least square technique. Comparison results of root mean square error for different fractional orders are also presented.
MODELING EARTH SYSTEMS AND ENVIRONMENT
(2023)
Article
Mathematics, Applied
F. Abdolabadi et al.
Summary: In this paper, a split-step Fourier pseudo-spectral method is proposed for solving the space fractional coupled nonlinear Schrodinger equations. The method splits the equations into two subproblems, with one of them being linear. The solution for the nonlinear subproblem is computed exactly, and the Riesz space fractional derivative is approximated using a Fourier pseudo-spectral method. The stability, convergence, discrete charge, and multi-symplectic preserving properties of the proposed method are investigated, and it is extended for solving two-dimensional problems. Numerical experiments are conducted to validate the theoretical analysis and demonstrate the efficiency of the proposed scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Hengfei Ding et al.
Summary: In this paper, a new generating function is constructed and used to establish a fourth-order numerical differential formula for approximating the Riesz derivative with order gamma is an element of (1, 2]. The formula is then applied to study the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equation and a convergence order of O(tau 2 + h4x + h4) is obtained. The unique solvability, unconditional stability, and convergence of the numerical algorithm are proved using discrete energy method and newly derived discrete fractional Sobolev embedding inequalities. Numerical results confirm the theoretical correctness and effectiveness of the proposed scheme. (c) 2023 Elsevier B.V. All rights reserved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Hengfei Ding et al.
Summary: This paper focuses on developing a high-order and structure-preserving numerical algorithm for the two-dimensional nonlinear space fractional Schrodinger equations. A fourth-order numerical differential formula is obtained by constructing a new generating function to approximate the spatial Riesz derivative, while the Crank-Nicolson method is used for the time derivative. The conservation, solvability, and convergence of the numerical algorithm are proven based on the energy method. Numerical examples are provided to verify the theoretical analysis and the validity of the numerical algorithm.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Minling Zheng et al.
Summary: The study utilizes a matrix transfer technique combined with spectral/element method to solve fractional diffusion equations involving the fractional Laplacian, and analyzes the convergence of the MTT method. Numerical results demonstrate exponential convergence in spatial discretization, in accordance with theoretical analysis, supporting the applicability of the method to solve various fractional equations involving the fractional Laplacian on complex domains.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Chaolong Jianig et al.
Summary: A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schrodinger equation. The methods reformulate the original equation into an equivalent form that satisfies a quadratic energy and apply the Fourier pseudo-spectral method to approximate the spatial derivatives. The proposed schemes produce numerical solutions that precisely conserve the modified energy and are more efficient compared to other existing structure-preserving schemes.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Rui-lian Du et al.
Summary: This article presents a finite difference scheme for a variable-order time-fractional wave partial differential equation, which has stability and convergence properties. Numerical experiments are conducted to validate the theoretical analysis and demonstrate the computational efficiency of the scheme.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Marziyeh Saffarian et al.
Summary: In this paper, an efficient numerical method for solving Riesz space fractional advection-dispersion equation is proposed by combining the Crank-Nicolson scheme and spectral element method. The stability of the scheme is proven and numerical results demonstrate its accuracy and efficiency compared to other schemes in literature.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Hengfei Ding et al.
Summary: The main goal of this paper is to construct high-order numerical differential formulas for approximating the Riesz derivative and apply them to the numerical solution of the nonlinear space fractional Ginzburg-Landau equations. The paper introduces a novel second-order fractional central difference operator and a novel fourth-order fractional compact difference operator. It also develops new techniques and important lemmas to prove the unique solvability, stability, and convergence of the proposed difference scheme. Numerical examples demonstrate the efficiency and accuracy of the methods.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Review
Mathematics, Applied
Duy Phan et al.
Summary: This paper considers two types of second-order in time partial differential equations, namely semilinear wave equations and semilinear beam equations. To solve these equations with exponential integrators, an approach to efficiently compute the action of the matrix exponential and related matrix functions is presented. Various numerical simulations are provided to illustrate the effectiveness of this approach.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
A. Devi et al.
Journal of Scientific Research
(2021)
Article
Computer Science, Interdisciplinary Applications
Ruize Yang et al.
Summary: In this paper, a family of second and third order temporal integration methods for stiff ordinary differential equations is proposed, combining traditional Runge-Kutta and exponential Runge-Kutta methods to preserve sign and steady-state properties. These methods are applied with well-balanced discontinuous Galerkin spatial discretization to solve nonlinear shallow water equations with friction terms. The fully discrete schemes are demonstrated to satisfy well-balanced, positivity-preserving, and sign-preserving properties simultaneously, showing good numerical results on various test cases.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Jin Cui et al.
Summary: A family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods were developed for the nonlinear Schrodinger equation by combining the scalar auxiliary variable approach with the exponential Runge-Kutta method. By introducing an auxiliary variable and applying the Lawson method and the symplectic Runge-Kutta method in time, a class of mass and energy-preserving time-discrete schemes were derived which are arbitrarily high-order in time. Numerical experiments demonstrated the accuracy and effectiveness of the newly proposed schemes.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Lu Zhang et al.
JOURNAL OF SCIENTIFIC COMPUTING
(2020)
Article
Mathematics, Applied
Qifeng Zhang et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2020)
Article
Mathematics, Interdisciplinary Applications
Jingwei Hu et al.
MULTISCALE MODELING & SIMULATION
(2019)
Article
Mathematics, Applied
S. Mohammadian et al.
Article
Mathematics, Applied
Han Zhou et al.
JOURNAL OF SCIENTIFIC COMPUTING
(2013)
Article
Mathematics, Applied
F. Liu et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2012)
Article
Computer Science, Interdisciplinary Applications
Cem Celik et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2012)
Article
Engineering, Multidisciplinary
Q. Yang et al.
APPLIED MATHEMATICAL MODELLING
(2010)
Article
Mathematics
Marlis Hochbruck et al.
Article
Computer Science, Interdisciplinary Applications
Mingrong Cui
JOURNAL OF COMPUTATIONAL PHYSICS
(2009)
Article
Computer Science, Software Engineering
Havard Berland et al.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2007)
Article
Mathematics, Applied
ZZ Sun et al.
APPLIED NUMERICAL MATHEMATICS
(2006)
Article
Computer Science, Interdisciplinary Applications
S Krogstad
JOURNAL OF COMPUTATIONAL PHYSICS
(2005)
Article
Mathematics, Applied
AK Kassam et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2005)
Article
Mathematics, Applied
M Hochbruck et al.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2005)
Article
Statistics & Probability
E Orsingher et al.
PROBABILITY THEORY AND RELATED FIELDS
(2004)
Article
Mathematics
E Orsingher et al.
CHINESE ANNALS OF MATHEMATICS SERIES B
(2003)
Article
Mathematics, Applied
RC Cascaval et al.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2002)
Article
Computer Science, Interdisciplinary Applications
SM Cox et al.
JOURNAL OF COMPUTATIONAL PHYSICS
(2002)
