A combination method for numerical solution of the nonlinear stochastic Itô-Volterra integral equation

2021 ◽  
Vol 407 ◽  
pp. 126302
Author(s):  
Xiaoxia Wen ◽  
Jin Huang
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Volterra Integral Equation ◽  
Combination Method

scholarly journals Numerical Solution of a Non-Linear Volterra Integral Equation

2015 ◽  
Vol 44 (1) ◽  
pp. 5-28 ◽  
Author(s):  
K. Maleknejad ◽  
P. Torabi ◽  
S. Sauter
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Volterra Integral Equation ◽  
Non Linear

scholarly journals Numerical Solution of Multidimensional Stochastic Itô-Volterra Integral Equation Based on the Least Squares Method and Block Pulse Function

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ting Ke ◽  
Guo Jiang ◽  
Mengting Deng
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Least Squares ◽  
Algebraic Equation ◽  
Volterra Integral Equation ◽  
Linear Algebraic Equation ◽  
Least Squares Method ◽  
Numerical Examples ◽  
Block Pulse Function

In this paper, a method based on the least squares method and block pulse function is proposed to solve the multidimensional stochastic Itô-Volterra integral equation. The Itô-Volterra integral equation is transformed into a linear algebraic equation. Furthermore, the error analysis is given by the isometry property and Doob’s inequality. Numerical examples verify the effectiveness and precision of this method.

scholarly journals Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
K. Maleknejad ◽  
M. Khodabin ◽  
F. Hosseini Shekarabi
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Rate Of Convergence ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Volterra Integral Equations ◽  
Numerical Example ◽  
Block Pulse Functions ◽  
A New Technique ◽  
Modified Block

We present a new technique for solving numerically stochastic Volterra integral equation based on modified block pulse functions. It declares that the rate of convergence of the presented method is faster than the method based on block pulse functions. Efficiency of this method and good degree of accuracy are confirmed by a numerical example.

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