A novel numerical scheme for fractional differential equations using extreme learning machine

被引：20

作者：

Sivalingam, S. M. ^{[1
]}

Kumar, Pushpendra ^{[2
]}

Govindaraj, V. ^{[1
]}

机构：

[1] Natl Inst Technol Puducherry, Dept Math, Karaikal 609609, India

[2] Univ Johannesburg, Inst Future Knowledge, POB 524, ZA-2006 Auckland Pk, South Africa

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2023年 / 622卷

关键词：

Extreme learning machine; Neural networks; Legendre polynomials; Operational matrix; HOMOTOPY PERTURBATION METHOD; COLLOCATION METHOD; MATRIX;

D O I：

10.1016/j.physa.2023.128887

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically.& COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：21

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