In this paper, the boundary value inverse problem related to the generalized Burgers–Fisher and generalized Burgers–Huxley equations is solved numerically based on a spline approximation tool. B-splines with quasilinearization and Tikhonov regularization methods are used to obtain new numerical solutions to this problem. First, a quasilinearization method is used to linearize the equation in a specific time step. Then, a linear combination of B-splines is used to approximate the largest order of derivatives in the equation. By integrating from this linear combination, some approximations have been obtained for each of the functions and derivatives with respect to time and space. The boundary and additional conditions of the problem are also applied in these approximations. The Tikhonov regularization method is used to solve the system of linear equations using noisy data. Several numerical examples are provided to illustrate the accuracy and efficiency of the method.

中文翻译：

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广义Burgers–Fisher和广义Burgers–Huxley方程反问题的数值研究

在本文中，基于样条逼近工具用数值方法解决了与广义Burgers–Fisher方程和广义Burgers–Huxley方程有关的边值逆问题。具有拟线性化和Tikhonov正则化方法的B​​样条用于获得此问题的新数值解。首先，使用拟线性化方法在指定的时间步长内线性化方程。然后，使用B样条的线性组合来近似方程中的最大导数阶。通过对该线性组合进行积分，就时间和空间而言，每个函数和导数均获得了一些近似值。在这些近似中也应用了问题的边界和其他条件。Tikhonov正则化方法用于使用噪声数据求解线性方程组。提供了几个数值示例来说明该方法的准确性和效率。