Strong convergence and stability of the split-step theta method for highly nonlinear neutral stochastic delay integro differential equation

2020 ◽  
Vol 157 ◽  
pp. 385-404
Author(s):  
Jingjun Zhao ◽  
Yulian Yi ◽  
Yang Xu
Keyword(s):  
Differential Equation ◽  
Strong Convergence ◽  
Stochastic Delay ◽  
Integro Differential Equation ◽  
Convergence And Stability ◽  
Highly Nonlinear ◽  
Theta Method

scholarly journals Strong Convergence of the Split-Step Theta Method for Stochastic Delay Differential Equations with Nonglobally Lipschitz Continuous Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chao Yue ◽  
Chengming Huang
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Delay Differential Equations ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Lipschitz Continuous ◽  
Highly Nonlinear ◽  
Nonautonomous Equations ◽  
Delay Differential ◽  
Theta Method

This paper is concerned with the convergence analysis of numerical methods for stochastic delay differential equations. We consider the split-step theta method for nonlinear nonautonomous equations and prove the strong convergence of the numerical solution under a local Lipschitz condition and a coupled condition on the drift and diffusion coefficients. In particular, these conditions admit that the diffusion coefficient is highly nonlinear. Furthermore, the obtained results are supported by numerical experiments.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

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