Abstract
In this paper, a computational technique is introduced for the solution of the first order multi-pantograph differential equation (MPDE) through some well-known optimization algorithms like sequential quadratic programming (SQP) and Active Set Technique (AST). Furthermore, artificial neural network (ANN) is used for networking of the first order multi-pantograph differential equation in used to provide mathematical model based on unsupervised error for equation. Moreover, mathematical modeling has been performed perfectly through multi-runs for simulation to justify the better convergence of the solutions. Also, two examples are presented to exhibit the aptitude of the method SQP and AST. The comparative study will be made with reported techniques such as variational iteration technique (VIT) [6] and collocation based on Bernstein polynomial method (BCM) [6].
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