A linear Galerkin numerical method for a strongly nonlinear subdiffusion equation

07/21/2021
by   Łukasz Płociniczak, et al.
0

We couple the L1 discretization for Caputo derivative in time with spectral Galerkin method in space to devise a scheme that solves strongly nonlinear subdiffusion equations. Both the diffusivity and the source are allowed to be nonlinear functions of the solution. We prove method's stability and convergence with order 2-α in time and spectral accuracy in space. Further, we illustrate our results with numerical simulations that utilize parallelism for spatial discretization. Moreover, as a side result we find asymptotic exact values of error constants along with their remainders for discretizations of Caputo derivative and fractional integrals. These constants are the smallest possible which improves the previously established results from the literature.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/04/2021

On spectral Petrov-Galerkin method for solving fractional initial value problems in weighted Sobolev space

In this paper, we investigate a spectral Petrov-Galerkin method for frac...
research
06/09/2021

Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology

A special place in climatology is taken by the so-called conceptual clim...
research
09/15/2019

An L1 approximation for a fractional reaction-diffusion equation, a second-order error analysis over time-graded meshes

A time-stepping L1 scheme for subdiffusion equation with a Riemann–Liouv...
research
09/10/2021

Two-derivative deferred correction time discretization for the discontinuous Galerkin method

In this paper, we use an implicit two-derivative deferred correction tim...
research
11/03/2019

Numerical study of the transverse stability of the Peregrine solution

We numerically study the transverse stability of the Peregrine solution,...
research
06/02/2020

Large deviations principles for symplectic discretizations of stochastic linear Schrödinger Equation

In this paper, we consider the large deviations principles (LDPs) for th...
research
12/15/2019

On energy preserving high-order discretizations for nonlinear acoustics

This paper addresses the numerical solution of the Westervelt equation, ...

Please sign up or login with your details

Forgot password? Click here to reset