A Numerical Scheme for Time Fractional Stochastic Advection-Diffusion Equation with Vieta-Lucas Polynomials
Keywords:
Fractional stochastic Advection-Diffusion equation, Vieta-Lucas polynomials, Brownian motion, Operational matrixAbstract
In this paper, a numerical method is implemented to solve time fractional stochastic Advection-Diffusion equation. The aforementioned equation plays a pivotal role across a spectrum of applied sciences. Vieta-Lucas polynomials are employed as basic functions to achieve numerical solutions. The central idea of our method involves the approximation of Brownian motion via the application of Gauss-Legendre quadrature, thereby simplifying computational efforts. Within the framework of the proposed technique, operational matrices derived from the aforementioned polynomials are utilized. It is pertinent to note that the stochastic model under consideration is transformed into a simpler system via the application of the derived operational matrices. Subsequently, Newton's method is employed to ascertain the numerical solution for the specified model. Theoretical validation of the error bound and convergence analysis for the referenced scheme has been established. In addition, proofs pertaining to the existence and uniqueness of the solutions for the equation under investigation have been furnished. To demonstrate the precision and efficacy of the suggested approach, several test problems have been employed.
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