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CAS小波法求高阶弱奇异非线性积分微分方程数值解 被引量：3

CAS wavelet method for solving numerical solution of high order nonlinear integro-differential equation with weak singularity
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摘要 为了求高阶变系数且带有弱奇异积分核非线性Volterra-Fredholm积分微分方程的数值解,文章结合CAS小波的性质及block pulse函数,给出任意阶弱奇异积分的近似求积公式,同时也给出CAS小波的积分算子矩阵,进而可以化简所求非线性积分微分方程,将原问题转换为求非线性方程组的解,数值算例验证了该方法的有效性。 In order to obtain the numerical solution of high order variable coefficients nonlinear Volter- ra-Fredholm integro-differential equation with weakly singular kernels, an approximate formula which solves the solution of arbitrary order weakly singular integral is given by combining the properties of CAS wavelet and block pulse functions. And an integral operational matrix of CAS wavelet is also ob- tained. Then the original problem of the equation is translated irito solving a nonlinear system of alge- braic equations through simplifying and dispersing the nonlinear integro-differential equation. The nu- merical example shows that the method is effective.
作者 魏金侠 单锐 刘文 靳飞
机构地区 燕山大学理学院
出处 《合肥工业大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第9期1293-1296,共4页 Journal of Hefei University of Technology：Natural Science
基金 国家自然科学基金资助项目(50875230) 河北省教育厅科学研究计划资助项目(2009159)
关键词 高阶变系数 弱奇异 非线性 积分微分方程 CAS小波 BLOCK pulse函数 算子矩阵 数值解 high order variable coefficient weak singularity nonlinearity integro-differential equa- tion CAS wavelet block pulse function operational matrix numerical solution
分类号 O241.8 [理学—计算数学]
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参考文献9

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二级参考文献4

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共引文献2

同被引文献33

  • 1张阳,薛运华.求解一类高阶线性Fredholm积分微分方程的Tau方法[J].高等学校计算数学学报,2005,27(S1):1-5. 被引量：1
  • 2Sadek I. Abualrub T. Abukhaled M A computational method for solving optimal control of a system of parallel beams using Legendre wavelets[J]. Math Comput Model. 2007. 45(9/10): 1253-1264.
  • 3Bujurke N M. Shiralashetti S C. Salimath C S. An applica?tion of single-term Haar wavelet series in the solution of nonlinear oscillator equations[J].J Comput Appl Math. 2009.227(2):234-244.
  • 4Babolian E. Masouri Z. Hatamzadeh-Varmazyar S. Nu?merical solution of nonlinear Volterra-Fredholm integra-dif?ferential equations via direct method using triangular func?tions[J]. Computer &. Mathemtics with Applications. 2009.58(2): 239-247.
  • 5Kagani M. Vencheh A The Chebyshev wavelets opera?tional matrix of integration and product operation matrix[J]. Int Comput Math. 2008. 86(7):1118-1125.
  • 6Reihani M H. Abadi Z. Rationalized Haar functions meth?od for solving Fredholm and Volterra integral equations[J].J Comput Appl Math. 2007.200(1): 12-20.
  • 7Bujurke N M. Salimath C S. Shiralashetti S C. Numerical solution of stiff systems from nonlinear dynamics using sin?gle-term Haar wavelet series[J 1 Nonlinear Dynamics. 2008.51(4) :595-605.
  • 8Mahmoudi Y. Wavelet Galerkin method for numerical solu?tion of nonlinear integral equation[J]. Appl Math Cornput , 2005.167(2): 1119-1120.
  • 9Babolian E. Fattahzadeh F. Numerical solution of differen?tial equations by using Chebyshev wavelet operational ma?trix of integration[J 1 Appl Math Comput , 2007. 188 (1):417.
  • 10WUJ L A Wavelet operational method for solving frac?tional partial differential equations numerically[J]. Appl Math Comput , 2009.214(2) :31-40.

引证文献3

二级引证文献8

合肥工业大学学报（自然科学版）
2012年 第9期

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