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非线性二阶变系数微分方程的三点边值问题

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研究了非线性二阶变系数微分方程的三点边值问题.首先,对非线性二阶变系数微分方程多次积分得到与之等价的Fredholm-Hammerstein积分方程;其次,利用分段泰勒级数得到Fredholm-Hammerstein积分方程的数值解;最后,通过具体算例验证此方法的可行性与有效性,并给出相应的误差估计.
Three-point boundary value problems for nonlinear second-order variable coefficient differential equations
This paper deals with the three-point boundary value problem for nonlinear second-order variable coefficient differential equations.Firstly,the equivalent Fredholm-Hammerstein integral equations are obtained by integrating the non-linear second-order variable coefficient differential equations multiple times;secondly,the numerical solution of the Fred-holm-Hammerstein integral equations are gotten using piecewise taylor series;finally,the feasibility and effectiveness of this method are verified through specific examples,and corresponding error estimates are presented.

Nonlinear second-order variable coefficient differential equationThree-point boundary value problemFredholm-Hammerstein integral equationNumerical solutionIntegration method

刘雪铃、黄静

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亳州学院 电子与信息工程系,安徽 亳州 236800

非线性二阶变系数微分方程 三点边值问题 Fredholm-Hammerstein积分方程 数值解 积分法

安徽省教育厅自然科学研究重点项目安徽省教育厅自然科学研究项目

2022AH052415KJ2021A1150

2024

宁夏师范学院学报
宁夏师范学院

宁夏师范学院学报

影响因子：0.138
ISSN：1674-1331
年,卷(期)：2024.45(4)
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