Abstract
Parametric iteration method falls under the category of the analytic approximate methods for solving various kinds of nonlinear differential equations. Its convergence only for some special problems has been proved. However in this paper, an analysis of error is presented, then due to it, the convergence of method for general problems is proved. To assess the performance of the claimed error bound and also the convergence of the method, numerical experiments are presented performed in MATLAB 2012b.
Highlights
Parametric iteration method (PIM) is an analytic approximate method for solving linear and nonlinear problems proposed in [1]
Parametric iteration method falls under the category of the analytic approximate methods for solving various kinds of nonlinear differential equations
To assess the performance of the claimed error bound and the convergence of the method, numerical experiments are presented performed in MATLAB 2012b
Summary
Parametric iteration method (PIM) is an analytic approximate method for solving linear and nonlinear problems proposed in [1]. The work of Odibat [7] is more interesting and different because of its generality He concluded the convergence of the VIM by introducing a semi-contraction operator and completed the proof like the proof of the Banach’s fixed point theorem. [8,9]), but what is still missing is a proof of the convergence of the PIM for a general differential equation. From the both theoretical and practical viewpoint, another necessary talk is a complete discussion about the error bound of the approximations. (For more details about PIM see [1])
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