A novel stochastic ten non-polynomial cubic splines method for heat equations with noise term

Fareed, Aisha F.; Khattab, Ahmed G.; Semary, Mourad S.

doi:10.1016/j.padiff.2024.100677

Partial Differential Equations in Applied Mathematics

2024

DOI: 10.1016/j.padiff.2024.100677

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A novel stochastic ten non-polynomial cubic splines method for heat equations with noise term

Aisha F. Fareed,

Ahmed G. Khattab,

Mourad S. Semary

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2024

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Exploring Stochastic Heat Equations: A Numerical Analysis with Fast Discrete Fourier Transform Techniques

Khattab,

Semary,

Hammad

et al. 2024

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This paper presents an innovative numerical technique for specific classes of stochastic heat equations. Our approach uniquely combines a sixth-order compact finite difference algorithm with fast discrete Fourier transforms. While traditional discrete sine transforms are effective for approximating second-order derivatives, they are inadequate for first-order derivatives. To address this limitation, we introduce an innovative variant based on exponential transforms. This method is rigorously evaluated on two forms of stochastic heat equations, and the solutions are compared with those obtained using the established stochastic ten non-polynomial cubic-spline method. The results confirm the accuracy and applicability of our proposed method, highlighting its potential to enhance the numerical treatment of stochastic heat equations.

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Exploring Stochastic Heat Equations: A Numerical Analysis with Fast Discrete Fourier Transform Techniques

Khattab,

Semary,

Hammad

et al. 2024

Axioms

View full text Add to dashboard Cite

show abstract

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A novel stochastic ten non-polynomial cubic splines method for heat equations with noise term

Cited by 1 publication

References 38 publications

Exploring Stochastic Heat Equations: A Numerical Analysis with Fast Discrete Fourier Transform Techniques

Exploring Stochastic Heat Equations: A Numerical Analysis with Fast Discrete Fourier Transform Techniques

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