2017
DOI: 10.11121/ijocta.01.2017.00360
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Numerical solution of neutral functional-differential equations with proportional delays

Abstract: In this paper, homotopy analysis method is improved with optimal determination of auxiliary parameter by use of residual error function for solving neutral functional-differential equations (NFDEs) with proportional delays. Convergence analysis and error estimate of method are given. Some numerical examples are solved and comparisons are made with the existing results. The numerical results show that the homotopy analysis method with residual error function is very effective and simple.

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Cited by 14 publications
(10 citation statements)
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“…The optimal parameter of the known method by Liao (2010) was investigated [15]. It was utilized a variety of methods to calculate this ℎ parameter [7,10,18,23,[27][28][29].…”
Section: Optimal Homotopy Analysis Methodsmentioning
confidence: 99%
“…The optimal parameter of the known method by Liao (2010) was investigated [15]. It was utilized a variety of methods to calculate this ℎ parameter [7,10,18,23,[27][28][29].…”
Section: Optimal Homotopy Analysis Methodsmentioning
confidence: 99%
“…Equation (5.1) has an exact solution e −t [26]. Taking the natural transform of both side of (5.1) we obtain q .…”
Section: Analytical Examplesmentioning
confidence: 99%
“…Therefore, the fifth order approximation of the algorithm (3.14) converged to the exact solution of problem (5.1). This reduces the computational size used in [26] to obtain the approximate solution of the problem. The graph of the exact solution and fifth order approximate solution is plotted in Fig.…”
Section: Analytical Examplesmentioning
confidence: 99%
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“…Also, they stated that DDEs are a special kind of functional differential equations and finally solved these equations by presenting numerical methods. Sakar 3 improved the homotopy analysis method with optimal determination of auxiliary parameter by using residual error function for solving neutral functional‐differential equation with proportional delays. Öğrekçi 4 considered the stability problem of DDEs in the sense of Hyers‐Ulam‐Rassias, and he solved these equations by obtaining stability in unbounded intervals.…”
Section: Introductionmentioning
confidence: 99%