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On the numerical solution of stochastic quadratic integral equations via operational matrix method
Author(s) -
Mirzaee Farshid,
Samadyar Nasrin
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4907
Subject(s) - mathematics , nonlinear system , numerical integration , algebraic equation , rate of convergence , numerical analysis , matrix (chemical analysis) , collocation method , collocation (remote sensing) , quadratic equation , convergence (economics) , mathematical optimization , mathematical analysis , differential equation , computer science , ordinary differential equation , geometry , computer network , channel (broadcasting) , physics , materials science , quantum mechanics , machine learning , economic growth , economics , composite material
In this paper, stochastic operational matrix of integration based on delta functions is applied to obtain the numerical solution of linear and nonlinear stochastic quadratic integral equations (SQIEs) that appear in modelling of many real problems. An important advantage of this method is that it dose not need any integration to compute the constant coefficients. Also, this method can be utilized to solve both linear and nonlinear problems. By using stochastic operational matrix of integration together collocation points, solving linear and nonlinear SQIEs converts to solve a nonlinear system of algebraic equations, which can be solved by using Newton's numerical method. Moreover, the error analysis is established by using some theorems. Also, it is proved that the rate of convergence of the suggested method is O ( h 2 ). Finally, this method is applied to solve some illustrative examples including linear and nonlinear SQIEs. Numerical experiments confirm the good accuracy and efficiency of the proposed method.