A recursive integration method for approximate solution of stochastic differential equations

1998 ◽  
Vol 66 (1-2) ◽  
pp. 53-66 ◽  
Author(s):  
M. I. Abukhaled ◽  
E. J. Allen
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Integration Method ◽  
Recursive Integration

scholarly journals Caratheodory’s approximation for a type of Caputo fractional stochastic differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhongkai Guo ◽  
Junhao Hu ◽  
Weifeng Wang
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Explicit Expression ◽  
Existence And Uniqueness ◽  
Linear Growth ◽  
Growth Conditions ◽  
Uniqueness Of Solutions ◽  
Fractional Stochastic Differential Equations

AbstractThe Caratheodory approximation for a type of Caputo fractional stochastic differential equations is considered. As is well known, under the Lipschitz and linear growth conditions, the existence and uniqueness of solutions for some type of differential equations can be established. However, this approach does not give an explicit expression for solutions; it is not applicable in practice sometimes. Therefore, it is important to seek the approximate solution. As an extending work for stochastic differential equations, in this paper, we consider Caratheodory’s approximate solution for a type of Caputo fractional stochastic differential equations.

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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