The partially truncated Euler–Maruyama method for nonlinear pantograph stochastic differential equations

Zhan, Weijun; Gao, Yan; Guo, Qian; Yao, Xiaofeng

doi:10.1016/j.amc.2018.10.052

Cited by 7 publications

(2 citation statements)

References 17 publications

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“…The said equations have applicability in diverse range of subject areas, for instance, coherent states in quantum theory [2], control system [3] and cell-growth modeling in biology [4]. According to recent literature available, a number of numerical solvers have shown a great potential to solve [20], Laplace transform method [21], multistep block method [22], computational Legendre Tau method [23], fully-geometric mesh one-leg methods [24], Euler-Maruyama method [25]and so on. In all of these methods, the deterministic solution is generally given in different forms with stability and convergence analysis, while the outcomes show that all of these methods have their own limitations and advantages in comparison to others in certain applications.…”

Section: Introductionmentioning

confidence: 99%

Design of Neural Network With Levenberg-Marquardt and Bayesian Regularization Backpropagation for Solving Pantograph Delay Differential Equations

et al. 2020

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In this paper, novel computing paradigm by exploiting the strength of feed-forward artificial neural networks (ANNs) with Levenberg-Marquardt Method (LMM), and Bayesian Regularization Method (BRM) based backpropagation is presented to find the solutions of initial value problems (IVBs) of linear/nonlinear pantograph delay differential equations (LP/NP-DDEs). The dataset for training, testing and validation is created with reference to known standard solutions of LP/NP-DDEs. ANNs are implemented using the said dataset for approximate modeling of the system on mean squared error based merit functions, while learning of the adjustable parameters is conducted with efficacy of LMM (ANN-LMM) and BRMs (ANN-BRM). The performance of the designed algorithms ANN-LMM and ANN-BRM on IVPs of first, second and third order NP-FDEs are verified by attaining a good agreement with the available solutions having accuracy in the range from 10 -5 to 10 -8 and are further endorsed through error histograms and regression measures.

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Section: Introductionmentioning

confidence: 99%

Design of Neural Network With Levenberg-Marquardt and Bayesian Regularization Backpropagation for Solving Pantograph Delay Differential Equations

et al. 2020

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“…Hu et al [2] established the existence and uniqueness for a class of PSDEs. For more details, we refer the reader to [13,3,5,6,12] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Stability of Numerical Solution to Pantograph Stochastic Functional Differential Equations

Wu¹,

Hu²,

Chen³

2021

Preprint

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Stability of numerical solution to pantograph stochastic functional differential equations

Wu¹,

Hu²,

Chen

2022

Applied Mathematics and Computation

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The partially truncated Euler–Maruyama method for nonlinear pantograph stochastic differential equations

Cited by 7 publications

References 17 publications

Design of Neural Network With Levenberg-Marquardt and Bayesian Regularization Backpropagation for Solving Pantograph Delay Differential Equations

Design of Neural Network With Levenberg-Marquardt and Bayesian Regularization Backpropagation for Solving Pantograph Delay Differential Equations

Stability of Numerical Solution to Pantograph Stochastic Functional Differential Equations

Stability of numerical solution to pantograph stochastic functional differential equations

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