分数阶电报方程的Chebyshev多项式数值解法研究

Research of Numerical Methods for Solving Fractional-order Telegraph Equations Based on Chebyshev Polynomials

分数阶电报方程作为通信工程中的一类重要方程,在实际应用中往往很难求得解析解,因而对其进行数值求解就显得至关重要.为了求得分数阶电报方程的数值解,本文借助Chebyshev多项式函数构造相应的微分算子矩阵,并结合Tau方法将待求方程转化为非线性代数方程组,然后对该方程组进行数值离散求解,最后给出的数值算例也验证了该方法的可行性及有效性.

Fractional-order telegraph equation is regarded as one of most important equations in communication engineering, which is hard to obtain the analytical solution, so it is crucial to study the numerical methods. In order to obtain the numerical solutions of fractionalorder telegraph equations, this study derives the corresponding differential operational matrix through Chebyshev polynomials. Furthermore, the nonlinear telegraph equation is transformed into the system of algebra equations with known coefficients. Then, the numerical solutions can be obtained by solving the system. Lastly, the numerical example is proposed to verify the feasibility and effectiveness.