Further Application of Double Exponential Transformation

双指数变换的进一步应用

• 批准号: 20560060
• 负责人: AHNIYAZ Nurmuhammad
• 金额: $ 0.92万
• 依托单位: Tokyo Denki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20560060/
• 关键词: 数理工学(数理的解析・計画・設計・最適化); 二重指数変換; Double exponential transformation; DE-Sinc method; Sinc-collocation; 偏微分方程式; 初期値・境界値問題; 積分方程式; 特異摂動問題; 常微分方程式

In this study, the Sinc-Galerkin and the Sinc-collocation methods based on the double exponential transformation (DE transformation) for the second order singularly-perturbed boundary value problem of ordinary differential equation is considered. And the approximate solution for the partial differential equation is proposed. It is shown that the error behavior in these methods based on the DE transformation is (exp(-cN/log N)),c>0 where N is a parameter representing the number of terms in the Sinc approximation. High efficiency of the Sinc method based on the DE transformation is confirmed by some numerical examples of singularly-perturbed boundary value problem, and the numerical result exhibits higher efficiency than the one obtained by the Sinc method based on the single exponential (SE) transformation as N becomes large.

本文研究了二阶奇摄动常微分方程边值问题的SINC-Galerkin方法和基于双指数变换(DE变换)的SINC-配置法。给出了偏微分方程解的近似解。结果表明，在这些基于DE变换的方法中，误差行为是(exp(-Cn/logN))，c&gt；0，其中N是表示sinc近似中的项数的参数。奇异摄动边值问题的数值算例验证了基于DE变换的SINC方法的高效率，当N变大时，数值结果显示出比基于单指数(SE)变换的SINC方法更高的效率。

项目成果

DE-Sinc method for Second Order Singularly Perturbed Boundary Value Problem

求解二阶奇摄动边值问题的DE-Sinc方法

• 发表时间: 2009
• 期刊: Japan Journal of Industrial and Applied Mathematics Vol. 26. No. 1
• 作者: Masatake Mori;Ahniyaz Nurmu hammad;Mayinur Muhammad
• 通讯作者: Mayinur Muhammad

Numerical Solution of Integral equations Based on the DE-Sinc Approximation with Weight Function

基于权函数DE-Sinc近似的积分方程数值解

• 发表时间: 2008
• 作者: Ahniyaz Nurmuhammad;Masatake Mori;Fukada Yasuhito
• 通讯作者: Fukada Yasuhito