A Computational Matrix Method For Multi-Dimensional Stochastic Volterra Integral Equations

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DOI: https://doi.org/10.28924/2291-8639-24-2026-312
Published: Oct 5, 2026
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Edwin Yao Kutorzi, A Computational Matrix Method For Multi-Dimensional Stochastic Volterra Integral Equations, Int. J. Anal. Appl., 24 (2026), 312.

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Edwin Yao Kutorzi

Abstract

Euler wavelets are constructed using Euler polynomials, which generally contain fewer terms than those used in alternative wavelet methods. As a result, the corresponding operational matrices are sparser, enabling more efficient numerical computation. This paper provides a comprehensive comparison of existing approximation methods for stochastic Volterra integral equations with multi-dimensional Brownian motion. The proposed approach employs Euler wavelet approximation in combination with block-pulse functions (BPFs). The operational matrices associated with block-pulse functions enable the transformation of stochastic Volterra equations into algebraic equations. This methodology offers a direct and efficient computational strategy by converting the single-integral problem into a linear algebraic system that is straightforward to solve. Several numerical examples are included to illustrate the effectiveness and accuracy of the proposed method.

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References

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