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.