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<p>In this study, we propose a numerical method to address initial-boundary value problems associated with a class of nonlinear fractional delay stochastic partial differential equations (NFDSPDEs), where the fractional derivative is defined in the Caputo sense. A stepwise collocation method based on sixth-kind Chebyshev polynomials (SKCPs) is developed, leveraging their advantageous analytical properties. In each step, the original NFDSPDE is transformed into a non-delay stochastic equation, which is solved using the collocation framework. A comprehensive error analysis is provided to confirm the reliability of the proposed method. The accuracy and efficiency of the scheme are further demonstrated through several representative test cases.</p>

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Stepwise Chebyshev collocation approach for nonlinear fractional delay stochastic partial differential equations

  • 期刊论文

  • 发表日期：

    2026年1月30日

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  • Afshin Babaei

摘要

In this study, we propose a numerical method to address initial-boundary value problems associated with a class of nonlinear fractional delay stochastic partial differential equations (NFDSPDEs), where the fractional derivative is defined in the Caputo sense. A stepwise collocation method based on sixth-kind Chebyshev polynomials (SKCPs) is developed, leveraging their advantageous analytical properties. In each step, the original NFDSPDE is transformed into a non-delay stochastic equation, which is solved using the collocation framework. A comprehensive error analysis is provided to confirm the reliability of the proposed method. The accuracy and efficiency of the scheme are further demonstrated through several representative test cases.