Numerical solution of stochastic ordinary differential equations using HAAR wavelet collocation method

Shiralashetti, S. C.; Lamani, Lata

doi:10.1080/09720502.2021.1874085

Cited by 6 publications

(1 citation statement)

References 14 publications

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“…It is not always possible to obtain the exact solution of these equations easily. So, in these cases we rely on the suitable numerical methods such as explicit and implicit approximation schemes [2, 20-22, 29, 39], Runge-Kutta method [31-33, 40, 42], Monte Carlo method [8], weak Simpson method [1], and wavelets [18,36]. In recent years, some researchers used the operational matrices of wavelets to solve stochastic equations [11, 23-25, 34, 37, 38].…”

Section: Introductionmentioning

confidence: 99%

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

Shariati

Yaghouti

Alipanah³

2023

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%