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Article
High Accuracy Combination Method For Solving the Systems of Nonlinear Volterra Integral and Integro-differential Equations with Weakly Singular Kernels of the Second Kind
Mathematical Problems in Engineering
  • Xiaoming He, Missouri University of Science and Technology
  • Lu Pan
  • Tao Lü
Editor(s)
Milovanović, Gradimir V.
Abstract
This paper presents a high accuracy combination algorithm for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind. Two quadrature algorithms for solving the systems are discussed, which possess high accuracy order and the asymptotic expansion of the errors. By means of combination algorithm, we may obtain a numerical solution with higher accuracy order than the original two quadrature algorithms. Moreover an a posteriori error estimation for the algorithm is derived. Both of the theory and the numerical examples show that the algorithm is effective and saves storage capacity and computational cost.
Department(s)
Mathematics and Statistics
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2010 Hindawi Publishing, All rights reserved.
Publication Date
1-1-2010
Citation Information
Xiaoming He, Lu Pan and Tao Lü. "High Accuracy Combination Method For Solving the Systems of Nonlinear Volterra Integral and Integro-differential Equations with Weakly Singular Kernels of the Second Kind" Mathematical Problems in Engineering (2010)
Available at: http://works.bepress.com/xiaoming-he/34/