Solution of time‐fractional stochastic nonlinear sine‐Gordon equation via finite difference and meshfree techniques

In this article, we introduce a numerical procedure to solve time‐fractional stochastic sine‐Gordon equation. The suggested technique is based on finite difference method and radial basis functions interpolation. By using this algorithm, first time‐fractional stochastic nonlinear sine‐Gordon equatio...

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Vydáno v:Mathematical methods in the applied sciences Ročník 45; číslo 7; s. 3426 - 3438
Hlavní autoři: Mirzaee, Farshid, Rezaei, Shadi, Samadyar, Nasrin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Freiburg Wiley Subscription Services, Inc 15.05.2022
Témata:
Algorithms
Approximation
Brownian motion process
Differential equations
Elliptic functions
Finite difference method
Interpolation
Mathematical analysis
Meshless methods
Nonlinear systems
Radial basis function
radial basis functions
stochastic partial differential equations
time‐fractional stochastic sine‐Gordon equation
Trigonometric functions
ISSN:0170-4214, 1099-1476
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Shrnutí:In this article, we introduce a numerical procedure to solve time‐fractional stochastic sine‐Gordon equation. The suggested technique is based on finite difference method and radial basis functions interpolation. By using this algorithm, first time‐fractional stochastic nonlinear sine‐Gordon equation is converted to elliptic stochastic differential equations. Then, the meshfree method based on radial basis functions (RBFs) is used to approximate the obtained equation. In fact, the finite difference method is used to approximate the unknown function in the time direction and generalized Gaussian RBF is applied to estimate the obtained equation in the space direction. The most important advantage of this method is that the noise terms are simulated directly at the collocation points at each time step. By employing this method, the equation decreased to a nonlinear system of algebraic equations which can be solved simply. The obtained results of solving three examples confirm the validity and capability of the proposed solution.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7988