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A Mingled Tau-Finite Difference Method for Stochastic First-Order Partial Differential Equations

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Abstract

Herein, we offer a numerical spectral-FD solution to a one-dimensional linear first-order stochastic partial differential equation driven by multiplicative noise and analyze the results. An efficient tau algorithm is implemented to get a system of first-order ordinary differential equation and then the Euler-Maruyama method is applied followed by the Lagrangian Interpolation, consequently, we get a semi-analytic solution, we analyze the obtained distribution. The philosophy of utilization of the tau method is built on picking the Tchebyshev basis functions that suitable for discretizing the equation in the space variable. The convergence of the unknown expansion coefficients and the truncation error analysis of the suggested solution are investigated. This numerical study was essentially built on supposing that the solution to the underlying problem is separable. We end the study by exhibiting some numerical experiments to check the applicability and accuracy of the offered algorithm.

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Acknowledgements

The authors would like to thank Prof. Georgios C. Georgiou (University of Cyprus - Cyprus) for his advise in the implementation of the numerical results.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

    Y. H. Youssri

  2. Mathematics and Actuarial Science Department, American University in Cairo, New Cairo, 11835, Egypt

    M. M. Muttardi

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  1. Y. H. Youssri
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Correspondence to Y. H. Youssri.

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Youssri, Y.H., Muttardi, M.M. A Mingled Tau-Finite Difference Method for Stochastic First-Order Partial Differential Equations. Int. J. Appl. Comput. Math 9, 14 (2023). https://doi.org/10.1007/s40819-023-01489-4

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