Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators

被引：10

作者：

Montanelli, Hadrien ^{[1
]}

Bootland, Niall ^{[1
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2020年 / 178卷

基金：

欧洲研究理事会;

关键词：

Stiff PDEs; Exponential integrators; Fourier spectral methods; Chebfun; PROPAGATION ITERATIVE METHODS; RUNGE-KUTTA METHODS; HIGH-ORDER; SYSTEMS; IMPLICIT; INSTABILITY; WAVES;

D O I：

10.1016/j.matcom.2020.06.008

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Dozens of exponential integration formulas have been proposed for the high-accuracy solution of stiff PDEs such as the Allen-Cahn, Korteweg-de Vries and Ginzburg-Landau equations. We report the results of extensive comparisons in MATLAB and Chebfun of such formulas in 1D, 2D and 3D, focusing on fourth and higher order methods, and periodic semilinear stiff PDEs with constant coefficients. Our conclusion is that it is hard to do much better than one of the simplest of these formulas, the ETDRK4 scheme of Cox and Matthews. Crown Copyright (C) 2020 Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). All rights reserved.

引用

页码：307 / 327

页数：21

共 50 条

[1] Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators
Montanelli, Hadrien
Bootland, Niall
Mathematics and Computers in Simulation, 2020, 178 : 307 - 327
[2] The Hanle effect in 1D, 2D and 3D
Sainz, RM
Trujillo Bueno, J
SOLAR POLARIZATION, 1999, 243 : 143 - +
[3] Laser Solitons in 1D, 2D and 3D
Rosanov, Nikolay N.
Fedorov, Sergey, V
Veretenov, Nikolay A.
EUROPEAN PHYSICAL JOURNAL D, 2019, 73 (07):
[4] Laser Solitons in 1D, 2D and 3D
Nikolay N. Rosanov
Sergey V. Fedorov
Nikolay A. Veretenov
The European Physical Journal D, 2019, 73
[5] 3D, 2D, 1D - ADLER,DA
BERNSTEIN, JE
YOUNG CHILDREN, 1976, 31 (04): : 316 - 316
[6] RELIABLE ITERATIVE METHODS FOR SOLVING 1D, 2D AND 3D FISHER'S EQUATION
Salih, Othman Mahdi
Al-Jawary, Majeed Ahmed
IIUM ENGINEERING JOURNAL, 2021, 22 (01): : 138 - 167
[7] Simulations of the ripening of 3D, 2D and 1D objects
Bonafos, C
Colombeau, B
Carrada, M
Altibelli, A
Claverie, A
MATERIALS SCIENCE AND ENGINEERING B-SOLID STATE MATERIALS FOR ADVANCED TECHNOLOGY, 2002, 88 (2-3): : 112 - 117
[8] Synthesis of 1D, 2D, and 3D structures of phosphorus
Ji, Haifeng
Smith, Joshua
Hagaman, Daniel
ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, 2016, 252
[9] Separation of Xylene Isomers through Selective Inclusion: 1D → 2D, 1D → 3D, and 2D → 3D Assembled Coordination Polymers via β-Sheets
Nath, Karabi
Biradha, Kumar
CRYSTAL GROWTH & DESIGN, 2016, 16 (10) : 5606 - 5611
[10] Determining Geometric Primitives for a 3D GIS Easy as 1D, 2D, 3D?
Lonneville, Britt
Stal, Cornelis
De Roo, Berdien
De Wulf, Alain
De Maeyer, Philippe
2015 1ST INTERNATIONAL CONFERENCE ON GEOGRAPHICAL INFORMATION SYSTEMS THEORY, APPLICATIONS AND MANAGEMENT (GISTAM), 2015, : 135 - 140

← 1 2 3 4 5 →