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【摘要】：本文針對兩類帶弱奇異核四階積分微分方程,提出高精度的LegendreGalerkin譜方法進行求解。對于第一類時間方向含有一階偏導數(shù)的四階積分微分方程,通過采用CrankNicolson方法離散原方程,構造Jacobi數(shù)值積分和Legendre數(shù)值積分近似替代積分項;空間方向采用Legendre-Galerkin譜方法進行逼近,得到第一類方程相應的稀疏離散代數(shù)系統(tǒng)。數(shù)值結果表明該方法具有有效性和長時間計算穩(wěn)定性。對于第二類時間方向含有二階偏導數(shù)的四階積分微分方程,通過對時間方向采用二階中心差分格式離散原方程,構造Jacobi數(shù)值積分和Legendre數(shù)值積分近似替代積分項;空間方向采用Legendre-Galerkin譜方法進行逼近,得到第二類方程相應的稀疏離散代數(shù)系統(tǒng)。數(shù)值結果表明該方法是有效的。
[Abstract]:In this paper, two kinds of fourth order integro-differential equations with weakly singular kernels are solved by LegendreGalerkin spectral method with high accuracy. For the fourth order integro-differential equation with first order partial derivative in the first kind of time direction, the CrankNicolson method is used to discretize the original equation to construct the Jacobi numerical integral and Legendre numerical integral to replace the integral term. The space direction is approximated by Legendre-Galerkin spectrum method, and the sparse discrete algebraic system corresponding to the first kind of equation is obtained. The numerical results show that the method is effective and stable for a long time. For the fourth order integro-differential equation with second order partial derivative in the second kind, Jacobi numerical integral and Legendre numerical integral are constructed by using the second order central difference scheme to discretize the original equation in the time direction. The space direction is approximated by Legendre-Galerkin spectrum method, and the sparse discrete algebraic system corresponding to the second kind of equation is obtained. Numerical results show that the method is effective.
【學位授予單位】：華僑大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241.8

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本文編號：2301713