应用数学2026，Vol.39Issue(2)：342-359,18.
非均匀网格上一维椭圆与抛物型方程的四阶紧有限体积方法
Fourth Order Compact Finite Volume Methods for 1D Elliptic and Parabolic Equations on Non-uniform Meshes
周磊 1王凤 2王同科2
作者信息
- 1. 天津财经大学珠江学院数据工程学院,天津 301811
- 2. 天津师范大学数学科学学院,天津 300387
- 折叠
摘要
Abstract
This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by dis-cretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.关键词
两点边值问题/抛物型方程/Robin边界条件/非均匀网格/四阶紧有限体积格式/预测-校正方法/误差估计Key words
Two point boundary value problem/Parabolic equation/Robin boundary condition/Non-uniform mesh/Fourth order compact finite volume scheme/Prediction-correction method/Error estimate分类
数理科学引用本文复制引用
周磊,王凤,王同科..非均匀网格上一维椭圆与抛物型方程的四阶紧有限体积方法[J].应用数学,2026,39(2):342-359,18.
