Numerical treatments for solving nonlinear mixed integral equation

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• 作者：M.A. Abdou^a ; ^{abdella777@yahoo.com} ; M. Basseem^b ; ^{basseem777@yahoo.com}
• 关键词：Mixed type of integral equation ; Nonlinear algebraic system (NLAS) ; Logarithmic kernel ; Carleman kernel ; Toeplitz matrix
• 刊名：Alexandria Engineering Journal
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：55
• 期：4
• 页码：3247-3251
• 全文大小：366 K
• 卷排序：55

文摘

We consider a mixed type of nonlinear integral equation (MNLIE) of the second kind in the space C[0,T]×L2(Ω),T<1C[0,T]×L2(Ω),T<1. The Volterra integral terms (VITs) are considered in time with continuous kernels, while the Fredholm integral term (FIT) is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs) with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.