An operational matrix method based on scalingfunction of Daubechies wavelet to solve stochastic differential equations

Abstract

In our joint work, by introducing Quasi Block-Pulse (QBP) functions,we provide integration and stochastic integration operational matricesbased on scaling function of Daubechies wavelet to solve linear and nonlinearstochastic differential equations. Due to interesting properties of theDaubechies wavelet such as orthogonality, compactly support and vanishingmoments, these operational matrices have good properties. The convergenceof the proposed method is presented and in order to verify the accuracy of theproposed method some numerical examples are provided.