Solving heat equations using extended B-spline alternating group explicit

THE 4TH INNOVATION AND ANALYTICS CONFERENCE & EXHIBITION (IACE 2019) Pub Date : 2019-08-21 DOI:10.1063/1.5121070

Nur Aliah Izzati Rosman, N. Hamid, Ahmad Abd. Majid, A. Ismail

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Abstract

In this paper, Extended B-Spline Alternating Group Explicit (ExtBSPAGE) iterative method is proposed to solve one- dimensional diffusion equation which is the heat conduction equation. The Alternating Group Explicit (AGE) iterative method is derived from the cubic Extended B-Spline collocation technique. We only consider the stationary case with odd number of points with even number of interval for both time and space dimension. The comparison will be made based on AGE, Cubic B-Spline Alternating Group Explicit (BSPAGE), ExtBSPAGE iterative method and the exact solution.In this paper, Extended B-Spline Alternating Group Explicit (ExtBSPAGE) iterative method is proposed to solve one- dimensional diffusion equation which is the heat conduction equation. The Alternating Group Explicit (AGE) iterative method is derived from the cubic Extended B-Spline collocation technique. We only consider the stationary case with odd number of points with even number of interval for both time and space dimension. The comparison will be made based on AGE, Cubic B-Spline Alternating Group Explicit (BSPAGE), ExtBSPAGE iterative method and the exact solution.

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用扩展b样条交替组显式求解热方程

本文提出了扩展b样条交替群显式(ExtBSPAGE)迭代法求解一维扩散方程即热传导方程。交替群显式迭代法(AGE)是由三次扩展b样条配置技术衍生而来的。在时间和空间维度上，我们只考虑奇数点和偶数间隔的平稳情况。将基于AGE、三次b样条交替群显式(BSPAGE)、ExtBSPAGE迭代法和精确解进行比较。本文提出了扩展b样条交替群显式(ExtBSPAGE)迭代法求解一维扩散方程即热传导方程。交替群显式迭代法(AGE)是由三次扩展b样条配置技术衍生而来的。在时间和空间维度上，我们只考虑奇数点和偶数间隔的平稳情况。将基于AGE、三次b样条交替群显式(BSPAGE)、ExtBSPAGE迭代法和精确解进行比较。

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THE 4TH INNOVATION AND ANALYTICS CONFERENCE & EXHIBITION (IACE 2019)

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