Numerical Approximations for the Tempered Fractional Laplacian: Error Analysis and Applications

Siwei Duo; Yanzhi Zhang

doi:10.1007/s10915-019-01029-7

Numerical Approximations for the Tempered Fractional Laplacian: Error Analysis and Applications

Siwei Duo
, Yanzhi Zhang

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we propose an accurate finite difference method to discretize the d-dimensional (for d ≥ 1) tempered integral fractional Laplacian and apply it to study the tempered effects on the solution of problems arising in various applications. Compared to other existing methods, our method has higher accuracy and simpler implementation....

Original language	American English
Journal	Journal of Scientific Computing
Volume	81
DOIs	https://doi.org/10.1007/s10915-019-01029-7
State	Published - Oct 1 2019

Keywords

Error Estimates
Finite Difference Methods
Fractional Allen-Cahn Equation
Fractional Gray-Scott Equations
Tempered Integral Fractional Laplacian

Disciplines

Mathematics
Statistics and Probability

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https://doi.org/10.1007/s10915-019-01029-7

Cite this

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title = "Numerical Approximations for the Tempered Fractional Laplacian: Error Analysis and Applications",

abstract = " In this paper, we propose an accurate finite difference method to discretize the d-dimensional (for d ≥ 1) tempered integral fractional Laplacian and apply it to study the tempered effects on the solution of problems arising in various applications. Compared to other existing methods, our method has higher accuracy and simpler implementation....",

keywords = "Error Estimates, Finite Difference Methods, Fractional Allen-Cahn Equation, Fractional Gray-Scott Equations, Tempered Integral Fractional Laplacian",

author = "Siwei Duo and Yanzhi Zhang",

year = "2019",

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day = "1",

doi = "10.1007/s10915-019-01029-7",

language = "American English",

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T1 - Numerical Approximations for the Tempered Fractional Laplacian: Error Analysis and Applications

AU - Duo, Siwei

AU - Zhang, Yanzhi

PY - 2019/10/1

Y1 - 2019/10/1

N2 - In this paper, we propose an accurate finite difference method to discretize the d-dimensional (for d ≥ 1) tempered integral fractional Laplacian and apply it to study the tempered effects on the solution of problems arising in various applications. Compared to other existing methods, our method has higher accuracy and simpler implementation....

AB - In this paper, we propose an accurate finite difference method to discretize the d-dimensional (for d ≥ 1) tempered integral fractional Laplacian and apply it to study the tempered effects on the solution of problems arising in various applications. Compared to other existing methods, our method has higher accuracy and simpler implementation....

KW - Error Estimates

KW - Finite Difference Methods

KW - Fractional Allen-Cahn Equation

KW - Fractional Gray-Scott Equations

KW - Tempered Integral Fractional Laplacian

UR - https://scholarsmine.mst.edu/math_stat_facwork/984

UR - https://doi.org/10.1007/s10915-019-01029-7

U2 - 10.1007/s10915-019-01029-7

DO - 10.1007/s10915-019-01029-7

M3 - Article

SN - 1573-7691

VL - 81

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

ER -

Numerical Approximations for the Tempered Fractional Laplacian: Error Analysis and Applications

Abstract

Keywords

Disciplines

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