Method of Particular Solutions for Second-Order Differential Equation with Variable Coefficients via Orthogonal Polynomials

Author:

Xie Huantian1,Zhang Zhaozhong1,Jiang Ziwu1,Zhou Jianwei1ORCID

Affiliation:

1. School of Mathematics and Statistics, Linyi University, Linyi, 276000 Shandong, China

Abstract

In this paper, with classic Legendre polynomials, a method of particular solutions (MPS, for short) is proposed to solve a kind of second-order differential equations with a variable coefficient on a unit interval. The particular solutions, satisfying the natural Dirichlet boundary conditions, are constructed with orthogonal Legendre polynomials for the variable coefficient case. Meanwhile, we investigate the a-priori error estimates of the MPS approximations. Two a-priori error estimations in H 1 - and L -norms are shown to depict the convergence order of numerical approximations, respectively. Some numerical examples and convergence rates are provided to validate the merits of our proposed meshless method.

Funder

Natural Science Foundation of Shandong Province

Publisher

Hindawi Limited

Subject

Analysis

Reference39 articles.

1. The Finite Element Method for Elliptic Problems

2. Numerical analysis of an optimal control problem governed by the stationary Navier-Stokes equations with global velocity-constrained;H. F. Niu;Communications in Computational Physics,2018

3. Finite Element Approximation of Optimal Control Problem Governed by Space Fractional Equation

4. Spectral Methods in Fluid Dynamics

5. Spectral Galerkin approximation of optimal control problem governed by Riesz fractional differential equation

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3