TY - JOUR
T1 - A Numerical Method for Solving Stochastic Volterra-Fredholm Integral Equation
TT -
JF - IJMSI
JO - IJMSI
VL - 18
IS - 1
UR - http://ijmsi.ir/article-1-1440-en.html
Y1 - 2023
SP - 145
EP - 164
KW - Generalized hat functions
KW - Improved hat functions
KW - Stochastic operational matrix
KW - Stochastic Volterra-Fredholm integral equation
KW - Brownian motion.
N2 - In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and embeded in the equation to achieve a linear system of equations which give the expansion coefficients of the solution. We prove that the rate of the convergence is O(h2) and O(h4) for these two different bases under some conditions. Two examples are solved and the results are compared with those of block pulse functions method (BPFs) to show the accuracy and reliability of the methods.
M3 10.52547/ijmsi.18.1.145
ER -