Toeplitz matrix method and nonlinear integral equation of Hammerstein type |
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Authors: | MA Abdou MM El-Borai MM El-Kojok |
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Institution: | 1. Alexandria University, Faculty of Education, Department of Mathematics, Alexandria, Egypt;2. Alexandria University, Faculty of Science, Department of Mathematics, Alexandria, Egypt |
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Abstract: | The existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated. |
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Keywords: | 45 B 05 45 G 10 65 R |
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