2019
DOI: 10.1002/mma.6045
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Abstract: In this paper, we suggest a convergent numerical method for solving nonlinear delay Volterra integro‐differential equations. First, we convert the problem into a continuous‐time optimization problem and then use a shifted pseudospectral method to discrete the problem. Having solved the last problem, we can achieve the pointwise and continuous approximate solutions for the main delay Volterra integro‐differential equations. Here, we analyze the convergence of the method and solve some numerical examples to show… Show more

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Cited by 6 publications
(2 citation statements)
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References 26 publications
(49 reference statements)
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“…We fully show that the approximate solutions are convergent to the exact solution when the number of collocation points tends to infinity. Note that spectral collocation methods have high accuracy and exponential convergence and, up to now many researchers utilized them to solve different continuous-time problems involving the ordinary and partial differential equations [12,13,18].…”
Section: Introductionmentioning
confidence: 99%
“…We fully show that the approximate solutions are convergent to the exact solution when the number of collocation points tends to infinity. Note that spectral collocation methods have high accuracy and exponential convergence and, up to now many researchers utilized them to solve different continuous-time problems involving the ordinary and partial differential equations [12,13,18].…”
Section: Introductionmentioning
confidence: 99%
“…They reduce their equation to a system of algebraic equations. Mahmoudi et al 12 used spectral collocation methods to numerically solve nonlinear delay Volterra integro‐differential equations. They converted their problem into the continuous‐time optimization problem and then approximated the optimal solution by using a interpolating polynomial.…”
Section: Introductionmentioning
confidence: 99%