Journal
APPLIED MATHEMATICAL MODELLING
Volume 37, Issue 10-11, Pages 6609-6616Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2012.09.075
Keywords
Singular integro-differential equation; Bernstein polynomial; Legendre wavelets; Operational matrix of integration
Funding
- Department of Science and Technology of the Government of India
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In this paper we study the numerical solution of singular Abel-Volterra integro-differential equations, which are typical for the theory of anomalous diffusion and viscoelastic delayed stresses. The proposed method is based on application of the operational and almost operational matrices to derivatives and integrals in a vicinity of the kernel's singular point. As examples, two orthonormal systems are considered: Bernstein polynomials and Legendre wavelets. The methods convert the singular integro-differential equation in to a system of algebraic equations that implies two advantages: (i) one does not need to introduce artificial smoothing factors into the singular integrand and (ii) the direct estimation of computational error around singular point is possible via the obtained explicit expression. The examples of numerical solution and their discussion are presented. (C) 2012 Elsevier Inc. All rights reserved.
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