D. Uma, H. Jafari, S. Raja Balachandar, S. G. Venkatesh, S. Vaidyanathan
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引用次数: 0
摘要
本文利用二维移位 Legendre 多项式（2DSLP）近似法求得了随机 Fitzhugh-Nagumo 偏微分方程的近似解。证实了问题的适用性和可解性。对提出的方法进行了收敛性分析和规范误差分析。使用 Maple 软件创建并实施了一种算法，以获得数值解。将获得的解与精确解以及使用显式阶 RK1.5 方法获得的解进行了比较。
An approximate solution for stochastic Fitzhugh–Nagumo partial differential equations arising in neurobiology models
In this paper, approximate solutions for stochastic Fitzhugh–Nagumo partial differential equations are obtained using two-dimensional shifted Legendre polynomial (2DSLP) approximation. The problem's suitability and solvability are confirmed. The convergence analysis for the proposed methodology and the error analysis in the
norm are carried out. Using Maple software, an algorithm is created and implemented to arrive at the numerical solution. The solution thus obtained is compared with the exact solution and the solution obtained using the explicit order RK1.5 method.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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