Projection-iterated method for solving numerically the nonlinear mixed integral equation in position and time

In this work, we consider a nonlinear Volterra-Hammerstein integral equation of the second kind ( V-HIESK ). The existence of a unique solution to the integral equation, under certain conditions, is guaranteed. The projection method was used, as the best numerical method. This method is better than...

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Vydáno v:Journal of Umm Al-Qura University for Applied Sciences Ročník 9; číslo 2; s. 107 - 114
Hlavní autor: Al Hazmi, Sharifah E.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.06.2023
Témata:
Chemistry
Chemistry and Materials Science
Chemistry/Food Science
Earth Sciences
Environmental Science and Engineering
Mathematics
Original Article
Physics
Statistics
Estimate error
Projection-iteration method
Volterra-Hammerstein integral equation
Successive approximations method
ISSN:2731-6734, 1658-8185
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Popis
Shrnutí:In this work, we consider a nonlinear Volterra-Hammerstein integral equation of the second kind ( V-HIESK ). The existence of a unique solution to the integral equation, under certain conditions, is guaranteed. The projection method was used, as the best numerical method. This method is better than the previous methods in the possibility of obtaining the lowest relative error. The method of obtaining the best approximate solution, through the projection method, depends on presenting three consecutive algorithms and depends mainly on the method of iterative projection (P-IM). In each algorithm, we get the approximate solution and the corresponding relative error. Moreover, we demonstrated that the estimated error of P-IM in the first algorithm is better than that of the successive approximation method (SAM). Some numerical results were calculated, and the error estimate was computed, in each case. Finally, the numerical results have been compared between this method and previous research, and it is clear through the same examples that the relative error of the first algorithm is better than the comparative error in the other methods.
ISSN:2731-6734
1658-8185
DOI:10.1007/s43994-023-00025-w