TY - JOUR
ID - 29388
TI - Wilson wavelets for solving nonlinear stochastic integral equations
JO - Wavelet and Linear Algebra
JA - WALA
LA - en
SN - 2383-1936
AU - Mousavi, Bibi Khadijeh
AU - Askari Hemmat, Ataollah
AU - Heydari, Mohammad Hossien
AD - Department of Pure Mathematica, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
AD - Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
AD - Shiraz University of Technology, Shiraz,
Y1 - 2017
PY - 2017
VL - 4
IS - 2
SP - 33
EP - 48
KW - Wilson wavelets
KW - Nonlinear stochastic It^o-Volterra integral equation
KW - Stochastic operational matrix
DO - 10.22072/wala.2017.59458.1106
N2 - A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It\^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It\^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operational matrices of integration and stochastic integration, the problem under study is transformed to a system of nonlinear algebraic equations which can be simply solved to obtain an approximate solution for the main problem. Moreover, a new technique for computing nonlinear terms in such problems is presented. Furthermore, convergence of Wilson wavelets expansion is investigated. Several examples are presented to show the efficiency and accuracy of the proposed method.
UR - https://wala.vru.ac.ir/article_29388.html
L1 - https://wala.vru.ac.ir/article_29388_cab6f5111dc82287318b83ae253c9278.pdf
ER -