Abstract
We reconstruct the variational iteration method that we call, parametric iteration method (PIM). The purposed method was applied for solving nonlinear Volterra integrodifferential equations (NVIDEs). The solution process is illustrated by some examples. Comparisons are made between PIM and Adomian decomposition method (ADM). Also exact solution of the 3rd example is obtained. The results show the simplicity and efficiency of PIM. Also, the convergence of this method is studied in this work.
Highlights
It is well known that many events in scientific fields deal with integrodifferential equations
The nonlinear Volterra integrodifferential equations play a major role in many physical processes such as nanohydrodynamic [1], dropwise condensation [2], and biologic [3]
Ω will be in terms of h; we plot Ω curve, and according to these h curves, it is easy to discover the valid region of h, which corresponds to the line segments nearly parallel to the horizontal axis
Summary
It is well known that many events in scientific fields deal with integrodifferential equations. Liao purposed homotopy analysis method [8] and it is applied in many scientific problems [9, 10]; VIM was purposed by He [11]. PIM was applied successfully for solving boundary value problems [12]. We consider nonlinear integrodifferential equations as follows:. Some examples are given and we solve them using parametric iteration method and compare the obtained results with ADM results. In all these cases, the present technique worked excellently, as it will be shown in this study
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