scholarly journals Numerical Solution of Weakly Singular Ito-Volterra Integral Equations via Operational Matrix Method based on Euler Polynomials

2018 ◽  
Vol 4 (1) ◽  
pp. 91-104
Author(s):  
Farshid Mirzaee ◽  
Nasrin Samadyar; ◽  
◽  
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Matrix Method ◽  
Operational Matrix ◽  
Volterra Integral Equations ◽  
Euler Polynomials ◽  
Operational Matrix Method ◽  
Weakly Singular

A stochastic operational matrix method for numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations

2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Block Pulse Function

AbstractIn this article, hybrid Legendre block-pulse functions are implemented in determining the approximate solutions for multi-dimensional stochastic Itô–Volterra integral equations. The block-pulse function and the proposed scheme are used for deriving a methodology to obtain the stochastic operational matrix. Error and convergence analysis of the scheme is discussed. A brief discussion including numerical examples has been provided to justify the efficiency of the mentioned method.

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