Using triangular orthogonal functions for solving Fredholm integral equations of the second kind
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...), a.m.johansen@warwick.ac.uk (A.M. Johansen), v.b.tadic@bristol.ac.uk (V.B. Tadić). and, by iterating, one obtains f ðx0Þ ¼ gðx0Þ þ X1 n¼1 Z En Yn k¼1 Kðxk 1; xkÞ ! gðxnÞdx1:n; ð3Þ where xi:j , (xi,. ....
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Cites methods from "Using triangular orthogonal functio..."
...In recent years, several simple and accurate methods based on orthogonal basic functions, including wavelets, have been used to approximate the solution of integral equations (Akyz-Daciolu, 2004; Blyth et al., 2004; Alipanah and Dehghan, 2007; Babolian et al., 2008; Hsiao, 2009; Liu, 2009)....
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References
150 citations
"Using triangular orthogonal functio..." refers background or methods in this paper
...The operational matrix for integration of BPFs has been derived as the following upper triangular matrix [8]:...
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...As proposed by many authors, specially in [8], a set of block pulse functions (BPFs) are usually defined in the interval 1⁄20; 1Þ as /iðtÞ 1⁄4 1 i m 6 t < iþ1 m ; 0 otherwise; ð1Þ where i 1⁄4 0; 1; ....
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90 citations
"Using triangular orthogonal functio..." refers background in this paper
...For more details about triangular orthogonal functions, see [1]....
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...The main body of Section 2 is based on [1]....
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...The authors of [1] called T1ðtÞ the left-handed triangular functions (LHTF) and T2ðtÞ the right-handed triangular functions (RHTF)....
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"Using triangular orthogonal functio..." refers methods or result in this paper
...Spline functions and Haar wavelets are also applied for solving these problems in [7,2]....
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...1 t BPF method Method of [2] TF method Exact solution 0 0....
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...This example is also provided in [2], and we compare the results....
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