The Use of Modified Block Pulse Functions for Solving the Stochastic Volterra-Fredholm Integral Equations
Keywords:Keywords: Brownian Motion, Itô Integral, Stochastic Integration Operational Matrix, SV-FIEs, MBPFs.
Abstract. A computational method based on modified block pulse functions is proposed for solving numerically stochastic VolterraFredholm integral equations. We obtain stochastic integration operational matrix of modified block pulse functions on interval [0,1). Amodified block pulse functions and their stochastic integration operational matrix can be reduced to a linear upper triangular system. Then, the problem under study is transformed to a system of linear algebraic equations which can be used to obtain an approximate solution of stochastic VolterraFredholm integral equations. Furthermore, the rate of convergence is (?) and error analysis of the proposed method are investigated. The results show that the approximate solutions have a good of efficiency and accuracy.
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