The telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor’s series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method.

中文翻译：

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基于修正扩展三次B样条函数求解非线性时间分数电报方程的新数值方法

电报模型描述了电流和电压波可以在电线上反射，对称的波形可以沿着一条线形成。已经通过改进的扩展三次 B 样条 (MECBS) 方法对传输线上的这些电压和电流波进行了数值研究。B 样条函数具有逼近解的灵活性和高阶精度。这些函数还保留了对称性。采用MECBS和Crank Nicolson技术求解非线性时间分数电报方程。时间方向是在 Caputo 意义上离散的，而空间维度是由修改后的扩展三次 B 样条离散的。方程中的非线性由泰勒级数线性化。所提出的算法是无条件稳定和收敛的。