Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations
DG Prakasha, P Veeresha… - Computational and …, 2019 - Wiley Online Library
The numerical solutions for nonlinear fractional Gardner and Cahn‐Hilliard equations
arising in fluids flow are obtained with the aid of two novel techniques, namely, fractional …
arising in fluids flow are obtained with the aid of two novel techniques, namely, fractional …
Semi-implicit Galerkin–Legendre spectral schemes for nonlinear time-space fractional diffusion–reaction equations with smooth and nonsmooth solutions
For the first time in literature, semi-implicit spectral approximations for nonlinear Caputo time-
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …
Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations
Recently there has been a growing interest in designing efficient numerical methods for the
solution of fractional differential equations. The solutions of such equations in general …
solution of fractional differential equations. The solutions of such equations in general …
Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations
This paper develops and analyses a finite difference/spectral-Galerkin scheme for the
nonlinear fractional Schrödinger equations with Riesz space-and Caputo time-fractional …
nonlinear fractional Schrödinger equations with Riesz space-and Caputo time-fractional …
An efficient dissipation–preserving Legendre–Galerkin spectral method for the Higgs boson equation in the de Sitter spacetime universe
Since the emergence of numerical methods in mathematical modeling, fundamental
properties such as convergence, efficiency, computational accuracy, and stability have been …
properties such as convergence, efficiency, computational accuracy, and stability have been …
A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations
D Hu, W Cai, Y Song, Y Wang - Communications in Nonlinear Science and …, 2020 - Elsevier
In this paper, we numerically investigate the space fractional nonlinear damped wave
equation. We construct a novel high-accuracy dissipation-preserving finite difference …
equation. We construct a novel high-accuracy dissipation-preserving finite difference …
On the solution of a Riesz space-fractional nonlinear wave equation through an efficient and energy-invariant scheme
JE Macías-Díaz - International Journal of Computer Mathematics, 2019 - Taylor & Francis
In this work, we consider a damped hyperbolic partial differential equation in multiple spatial
dimensions with spatial partial derivatives of non-integer order. The equation under …
dimensions with spatial partial derivatives of non-integer order. The equation under …
An energy-preserving computational approach for the semilinear space fractional damped Klein–Gordon equation with a generalized scalar potential
Naturally preserving dissipative or conservative structures of a given continuous system in
discrete analogs is of high demand when designing numerical schemes for dissipative or …
discrete analogs is of high demand when designing numerical schemes for dissipative or …
A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach
Y Fu, W Cai, Y Wang - Applied Numerical Mathematics, 2021 - Elsevier
This paper aims to develop a linearly implicit structure-preserving numerical scheme for the
space fractional sine-Gordon equation, which is based on the newly developed invariant …
space fractional sine-Gordon equation, which is based on the newly developed invariant …
An effective dissipation-preserving fourth-order difference solver for fractional-in-space nonlinear wave equations
J Xie, Z Zhang - Journal of Scientific Computing, 2019 - Springer
In this paper, we devise an efficient dissipation-preserving fourth-order difference solver for
the fractional-in-space nonlinear wave equations. First of all, we present a detailed …
the fractional-in-space nonlinear wave equations. First of all, we present a detailed …