An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders
KeywordsHaar wavelet Fredholm integral equations Volterra integral equations First-order integro-differential equations Second-order integro-differential equations Fourth-order integro-differential equations
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AbstractIn this paper, a novel technique is being formulated for the numerical solution of integral equations (IEs) as well as integro-differential equations (IDEs) of first and higher orders. The present approach is an improved form of the Haar wavelet methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013). The proposed modifications resulted in computational efficiency and simple applicability of the earlier methods (Aziz and Sirajul- Islam, 2013, Siraj-ul-Islam et al., 2013). In addition to this, the new approach is being extended from IDEs of first order to IDEs of higher orders with initial- and boundaryconditions. Unlike the methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013) (where the kernel function is being approximated by two-dimensional Haar wavelet), the kernel function in the present case is being approximated by one-dimensional Haar wavelet. The modified approach is easily extendable to higher order IDEs. Numerical examples are being included to show the accuracy and efficiency of the new method.
(Revista) ISSN 0377-0427
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Integral Methods in Science and Engineering Progress in Numerical and Analytic Techniques /Constanda, Christian.; Bodmann, Bardo E.J.; Velho, Haroldo F. de Campos.; SpringerLink (Online service)edited by Christian Constanda, Bardo E.J. Bodmann, Haroldo F. de Campos Velho.