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Chu, Yu-Ming; Ullah, Saif; Ali, Muzaher; Tuzzahrah, Ghulam Fatima; Munir, Taj

Numerical investigation of Volterra integral equations of second kind using optimal homotopy asymptotic method. (English) Zbl 1510.65325

Appl. Math. Comput. 430, Article ID 127304, 14 p. (2022).
Summary: This investigation is concerned with the solutions of Volterra integral equations of second kind that have been determined by employing Optimal Homotopy Asymptotic method (OHAM). The existence and uniqueness of solutions are proved in this work. The obtained solutions are novel, and previous literature lacks such derivations. The convergence of the approximate solutions using the proposed method is investigated. Error’s estimation to the corresponding numerical scheme is also carried out. The reliability and accuracy of OHAM have been shown by comparison of our derived solutions with solutions obtained by other existing methods. The efficiency of the proposed numerical technique is exhibited through graphical illustrations, and results are drafted in tabular form for specific values of parameter to validate the numerical investigation.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations

Keywords:

Taylor series expansion; residual equation; auxiliary function; convergence analysis; error estimation
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Full Text: DOI

References:

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