| 非光滑时间分数阶齐次扩散方程的修正 |
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| 引用本文： | 王艳永,杨艳,闫玉斌.非光滑时间分数阶齐次扩散方程的修正[J].数学的实践与认识,2021(7):239-245. |
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| 作者姓名： | 王艳永 杨艳 闫玉斌 |
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| 作者单位： | 吕梁学院数学系;切斯特大学数学系 |
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| 基金项目： | 国家自然科学基金(11771184);山西省自然科学基金(201801D121010);山西省高等学校教学改革创新项目(J2020352);山西省高等学校科技创新项目(2020L0700);吕梁市重点研发项目(2020GXZDYF22) |
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| 摘 要： | 当初值不光滑时,时间分数阶齐次扩散方程数值方法的精度会下降.为了得到高阶时间收敛格式,提出加权移位的Grünwald-Letnikov的修正格式,运用Lubich的修正方法,得到非光滑时间分数阶齐次扩散方程的收敛阶仍为O(k2).最后,通过数值算例验证了数值计算结果与理论计算结果一致.
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| 关 键 词： | 分数阶导数 非光滑数据 误差估计 LAPLACE变换 |
Correction of Time Discretization Schemes for Diffusion Equations with the Nonsmooth Data |
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| WANG Yan-yong,YANG Yan,YAN Yu-bin.Correction of Time Discretization Schemes for Diffusion Equations with the Nonsmooth Data[J].Mathematics in Practice and Theory,2021(7):239-245. |
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| Authors: | WANG Yan-yong YANG Yan YAN Yu-bin |
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| Institution: | (Department of Mathematics,Luliang University,Luliang 033000,China;Department of Mathematics,University of Chester,Chester,CH24BJ,UK) |
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| Abstract: | When the initial value is not smooth,the accuracy of the numerical method for the time fractional homogeneous diffusion equation will decrease.In order to obtain the higher time convergence scheme,the weighted and shifted Grünwald-Letnikov ’s correction scheme is introduced,we prove that the convergence order of the nonsmooth time fractional homogenous diffusion equation is still O(k2) by using the lubich’s correction method.Finally,a numerical example is given to verify the agreement between the numerical results and the theoretical ones. |
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| Keywords: | fractional derivatives nonsmooth data error estimates Laplace transform point theory |
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