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An Explicit Finite Difference Scheme for Time-Fractional Stochastic Traveling Wave Equations Driven by Multiplicative White Noise | ||
| Control and Optimization in Applied Mathematics | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 02 مهر 1405 اصل مقاله (1.36 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2026.77231.1394 | ||
| نویسندگان | ||
| Priti Mojad1؛ Babasaheb Gavhane2؛ Shrikisan Gaikwad3؛ Kalyanrao Takale4؛ Chetan Shirore* 5 | ||
| 1Department of Mathematics, New Arts Commerce and Science College, Ahmednagar, affiliated to Savitribai Phule Pune University, Pune, India | ||
| 2Department of Mathematics, K. J. Somaiya College of Arts, Commerce and Science, Kopargaon, India | ||
| 3Department of Mathematics, New Arts Commerce and Science College, Ahmednagar, India | ||
| 4Department of Computer Science, Jaykranti College of Computer Science and Management, Pune, India | ||
| 5Department of Mathematics, K.R.T. Arts, B.H. Commerce and A.M. Science College, Nashik, India | ||
| چکیده | ||
| This work addresses the numerical approximation of the time-fractional stochastic traveling wave equation (TFSTWE) with a Caputo fractional derivative of order α ∈ (1, 2] driven by multiplicative space-time white noise. An explicit finite difference method (FDM) is constructed by discretizing the space domain. For the first time step, a mean-square stability bound and an error estimate of order O(∆t2-α + ∆x2) are derived under a restriction on ∆t that depends explicitly on ∆x, the diffusion coefficient K, and the fractional order α, while the noise intensity σ enters the mean-square growth constant; stability and convergence at later time levels are supported numerically. Comprehensive numerical experiments demonstrate the effectiveness and reliability of the proposed method, and the Python programming language is used to plot the approximate mean solution profiles in two and three dimensions. The outcomes confirm the suitability of the method for accurately solving TFSTWEs under stochastic perturbations and support the theoretical analysis. | ||
تازه های تحقیق | ||
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| کلیدواژهها | ||
| Explicit difference approximation؛ Fractional derivatives؛ Mean square method؛ Multiplicative white noise | ||
| مراجع | ||
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